Can you hear me now? Cell Phone
Accounts
Teacher Background Information: Cell phones
are a part of the lives of an ever-increasing number
of people all over the world. This lesson is the first in
a series of lessons, which investigates the
sustainability of cell phones and begins with an
examination of cell phone usage.
Goals: To access and review statistical concepts and
graphical representations to investigate the issues of
sustainability surrounding a personal electronics item
that they use every day
Objectives: Students will…
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

Estimate and rewrite large numbers
Calculate the mean of a given data set
Calculate the median, upper and lower
quartiles of a data set using algebraic and
graphical methods
Construct a box-and-whisker plot for a given
data set
Content Area:
Number sense
Mean
Median
upper and lower
quartiles
Cumulative frequency
graphs
box-and-whisker plots
Standards met:
NM-NUM.9-12.1
NM-DATA.9-12.1
NM-PROB.REP.PK-12.1
Time required:
1 x 45-60 minute class
period
Materials: (one per
student)
 calculator
 graph paper
 ruler/straightedge
Procedure:
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Project the overhead ‘cell phone interesting facts’.
Lead a discussion based upon how the information about cell phones
relates to the future and the three E’s of sustainability.
Students should draw some conclusions about this phenomenon and
how it will affect the economics, social equity and environment into the
future.
Explain to the students that they will be using data and some of their
math skills to more deeply analyze cell phone usage.
Hand out the student sheets.
Review the worksheet and answer any questions.
Give students time to complete the worksheet.
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Cell Phone Accounts: Student
Worksheet
Name:____________________________________ Class period:_________
Telephones > Mobile cellular (most recent) by country
Rank
Country
Amount
#1
China
547,286,000
__________
#2
India
296,080,000
__________
#3
United States
255,000,000
__________
#4
Russia
170,000,000
__________
#5
Brazil
120,980,000
__________
#6
Japan
107,339,000
__________
#7
Germany
97,151,000
__________
#8
Pakistan
88,020,000
__________
#9
Indonesia
81,835,000
__________
Italy
78,571,000
__________
#10
Amount (in millions)
1. Complete the last column in the chart above by writing the amount of cell
phones, in millions of phones, in each country, rounded to the nearest tenth
of a million.
2. Calculate the mean number of cell phone accounts (in millions) for this
list. Show your calculations.
3. Calculate the upper quartile (75%ile) and the lower quartile (25%ile), and
hence, calculate the Inter Quartile Range. Show all your calculations.
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4. Calculate the median number of cell phone accounts (in millions) for this
list. Show your work.
Construct a “box-and-whisker” plot to show your 5-point summary.
5. Construct a cumulative frequency graph for this list of country’s cell
phone accounts. Use graph paper supplied by your teacher.
Use this graph to estimate the median, the lower and upper quartiles (show
your work on the graph). Estimate the number of cell phones rounded to
the nearest million. Write your answers below.
Median: _______________
Upper Quartile: ________________
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Lower Quartile: ________________
Cell Phone Accounts: Student Worksheet
Teacher Answer Key
Telephones > Mobile cellular (most recent) by country
Rank
Country
Amount
#1
China
547,286,000
___547.3___
#2
India
296,080,000
___296.1___
#3
United States
255,000,000
___255.0___
#4
Russia
170,000,000
___170.0___
#5
Brazil
120,980,000
___121.0___
#6
Japan
107,339,000
___107.3___
#7
Germany
97,151,000
____97.1___
#8
Pakistan
88,020,000
____88.0___
#9
Indonesia
81,835,000
____81.8___
Italy
78,571,000
____78.6___
#10
Amount (in millions)
1. Complete the last column in the chart above by writing the amount of cell
phones, in millions of phones, in each country, rounded to the nearest tenth
of a million.
(see table above)
2. Calculate the mean number of cell phone accounts (in millions) for this
list. Show your calculations.
(547.3 + 296.1 + 255 + 170 + 121 + 107.3 + 97.1 + 88 + 81.8 + 78.6) =
1842.2/10 = 184.22 millions of cell phones
3. Calculate the upper quartile (75%ile) and the lower quartile (25%ile), and
hence, calculate the Inter Quartile Range. Show all your calculations.
547.3 296.1 255 170 121
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upper quartile = 255 million cell phones
107.3 97.1 88 81.8 78.6
lower quartile = 88 million cell phones
Inter Quartile Range = 255 – 88 = 167 million cell phones
4. Calculate the median number of cell phone accounts (in millions) for this
list. Show your work.
547.3 296.1 255 170 121 107.3 97.1 88 81.8 78.6
middle values are 121 & 107.3
Median = (121 + 107.3)/2 = 114.15 million cell phones
Construct a “box-and-whisker” plot to show your 5-point summary.
Min = 78.6
Q1 = 88
Median = 114.15
Q3 = 255
Max = 547.3
5. Construct a cumulative frequency graph for this list of country’s cell
phone accounts. Use graph paper supplied by your teacher.
Use this graph to estimate the median, the lower and upper quartiles (show
your work on the graph). Estimate the number of cell phones rounded to
the nearest million. Write your answers below.
(Answers will vary, but should fall within the following ranges) (Answers are
in Millions of cell phones.)
Median: ___215 - 245____
Upper Quartile: ____300 - 400___
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Lower Quartile: ____125 - 150____
Interesting facts about Cell Phones
 At the end of September 2006, the world's cell phone subscribers reached 2.5 billion,
from 2 billion in September 2005, representing the fastest adoption of half a billion
subscribers, one year.
 By the end of 2008, the world's cell phone subscribers will reach over 3.5 billion.
 Between the end of 1994 and the beginning of 2006 cell phone usage in the U.S. rose
from 25 million to 219.4 million.
 87% of the U.S. population owns a cell phone.
 The average user replaces her cell phone every 18 months.
 A student's mobile phone bill ranges from $41 to $60 per month, but 57.5% of
students are on family plans and don't pay the bills themselves.
 19% of U.S. Internet users access the web from their mobile devices.
 Cell phone ownership among 12- to 14-year-olds increased from 13 percent in
February 2002 to now more than 55 percent. More than 36 percent of all 11- to 14year-olds own their own cell phone, more than 14 percent own personal digital
assistants and more than 15 percent own a hand-held Internet device.
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Cell Phone Recycling
Content Area:
Goals: To use data about recycling of cell phones to
Assess or review operations with percents, converting
numbers from one unit of measure to another.
Objectives: Students will...
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
Demonstrate the ability to solve problems using
percents
Solve problems that require converting from
one unit of measure to a different unit of
measure
Solve word problems
Procedure:
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Operations with
percents
Unit conversions
Solving word
problems
Standards met:
NM-NUM.9-12.1
NM-MEA.9-12.2
NM-PROB.PK-12.2
Time required:
15 – 20 minutes
Materials: (per
student)
 Student
worksheet
 calculator.
Ask students if anyone has an old cell phone at
home.
Explain to students that small electronics are
becoming the fastest growing waste stream
that the world has to consider and although
recycling for cell phones is available, not many people are currently
recycling their phones.
Hand out the students worksheets
Review the worksheet and answer any questions.
Give students time to complete the worksheet.
Have students go to the following webpage and watch the U-Tube
video.
http://www.eco-cell.org/cellwaste.asp
Then read the article at the following webpage.
http://www.eco-cell.org/egad.pdf
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Cell Phone Recycling: Student
Worksheet
Name:____________________________________ Class period:_________
Mobile Phones in Use: Worldwide, by Country
(This is only a partial list.)
Rank Country
Cell phones
Date of information
1. World
4,100,000,000
12/2008
2. China
710,000,000
8/2009
3. India
456,744,000
8/2009
4. United States
271,000,000
12/2008
Data collected from the following sources: http://www.epa.gov/epaoswer/education/pdfs/life-cell.pdf and www.eco-cell.org
The world wide rate for recycling cell phones is about 1%, while in the
United States the recycling rate for cell phones is about 5%.
Use the information above to answer the following questions.
1.
Approximately how many cell phones might you expect will be recycled
worldwide? How many in the United States?
2.
One cell phone recycling company, Falconbridge Ltd., estimated that it
can extract approximately 3.9 metric tons of gold from 130 million cell
phones. Calculate the following.
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3.9 metric tons
= ___________________kg
_______________ kg = ___________________ grams
_______________ g
_______________ oz
= ___________________ ounces
÷ 130,000,000
= __________________ ounces of gold in each cell phone.
3.
On October 15, 2009 gold was selling at $1050 per ounce.
value of the gold found in the average cell phone.
Find the
4.
On average, cell phones in the US are taken out of service after 1.5
years.
a.
If all cell phones are retired in 1.5 years, then how many will be
retired in 1 year?
b.
How many metric tons of gold are contained in the cell phones
retired each year?
c.
What is the market value of the gold extracted from retired cell
phones?
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d.
Based on your answer in part c,
i.
find the value of recycled cell phone gold (5%)
ii.
find the value of cell phone gold buried in landfills (20%)
iii.
Find the value of the gold in phones laying around the
house (75%)
5.
On average, 3 million metric tons of crushed rock is mined to recover
the 3.9 metric tons of gold found in 130,000,000 recycled cell phones.
How many metric tons of crushed rock from mining gold could be
avoided if all US cell phones were recycled?
6.
Why/how is recycling cell phones good for the environment?
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Cell Phone Recycling: Student
Worksheet: Teacher Key
Name:____________________________________ Class period:_________
Mobile Phones in Use: Worldwide, by Country
(This is only a partial list.)
Rank Country
Cell phones
Date of information
1. World
4,100,000,000
12/2008
2. China
710,000,000
8/2009
3. India
456,744,000
8/2009
4. United States
271,000,000
12/2008
Data collected from the following sources: http://www.epa.gov/epaoswer/education/pdfs/life-cell.pdf and www.eco-cell.org
The world wide rate for recycling cell phones is about 1%, while in the
United States the recycling rate for cell phones is about 5%.
Use the information above to answer the following questions.
1.
Approximately how many cell phones might you expect will be recycled
worldwide? How many in the United States?
4,100,000,000 x 0.01
= 41,000,000
2.
One cell phone recycling company, Falconbridge Ltd., estimated that it
can extract approximately 3.9 metric tons of gold from 130 million cell
phones. Calculate the following.
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3.9 metric tons
= _____3,900_____kg
_____3,900___ kg = ______3,900,000_______ grams
3,900,000 ÷ 28.35____ g
__137,566.14_____ oz
= ____137,566.14_____ ounces
÷ 130,000,000
= ____0.00106_____ ounces of gold in each cell phone.
3.
On October 15, 2009 gold was selling at $1050 per ounce.
value of the gold found in the average cell phone.
Find the
0.00106 x 1050 = $1.11
4.
On average, cell phones in the US are taken out of service after 1.5
years.
a.
If all cell phones are retired in 1.5 years, then how many will be
retired in 1 year?
1.0/1.5 = 2/3
b.
(271,000,000) x
2
÷ 3 = 180,666,666 cell phones
How many metric tons of gold are contained in the cell phones
retired each year?
180,666,666 : x = 130,000,000 : 3.9
x = 5.42 metric tons of gold
c.
What is the market value of the gold extracted from retired cell
phones?
5.42 x 1,000 x 1,000 ÷ 28.35 = 191.181.7 oz gold
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191,181,7 x $1050 = $200,740,740
d.
Based on your answer in part c,
i.
find the value of recycled cell phone gold (5%)
$200,740,740 x 0.05 = $10,037,037
ii.
find the value of cell phone gold buried in landfills (20%)
$200,740,740 x 0.20 = $40,148,148
iii.
Find the value of the gold in phones laying around the
house (75%)
$200,740,740 x 0.75 = $150,555,555
5.
On average, 3 million metric tons of crushed rock is mined to recover
the 3.9 metric tons of gold found in 130,000,000 recycled cell phones.
How many metric tons of crushed rock from mining gold could be
avoided if all US cell phones were recycled?
Write a proportion: x : 5.42 = 130,000,000 : 3.9
x = 180,666,666 metric tons of rock per year
6.
Why/how is recycling cell phones good for the environment?
Answers will vary.
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Cell Phone Pollution
Teacher Background Information: The
following web site provides valuable information
in the form of a poster:
http://www.epa.gov/osw/education/pdfs/lifecell.pdf
Goals: To use information about cell phone
pollution to assess or review understanding of
problem solving that involves unit conversions
and analysis of their results.
Objectives: Students will…
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Solve problems using percents
Solve problems that involve unit
conversions
Analyze their results and make a prediction
about future outcomes
Content Area:
 Operations with
percents
 Problem solving
that involves unit
conversions
 analysis of students’
results to make a
prediction about
future outcomes
Standards met:
NM-NUM.9-12.2
NM-ALG.9-12.2
NM-PROB.PK-12.1
Time required:
20 – 30 minutes
Materials: (per student)
Calculator
Procedure: (for the teacher)

Have students review the article at the following web address
http://www.eco-cell.org/egad.pdf and watch the U-Tube video at
http://www.eco-cell.org/cellwaste.asp
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Hand out the student worksheets.
Review the worksheet and answer any questions.
Give students time to complete the worksheet.
After all students are finished, discuss the concept of e-waste and the
problems of worker exposure regarding the manufacture and dumping
of electronics in the developing world. You may use the following
YouTube and Teachertube videos to spark conversation on this issue.
http://www.youtube.com/watch?v=sl2j83LCHss
http://www.youtube.com/watch?v=0JZey9GJQP0
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http://www.teachertube.com/viewVideo.php?video_id=106619&title=WR3A_
__Fair_Trade_Recycling&vpkey=
http://www.greenpeace.org/international/photosvideos/videos/mexicanelect
ronicsproductiontoxics
Cell Phone Pollution: Student
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Worksheet
Name:____________________________________ Class period:_________
While e-waste consists of discarded computers, cell phones, and other
electronic devices – let’s look at some data concerning cell phones in the
United States. Based upon a report by Inform, an environmental research
organization, the average cell phone is in use for only 18 months. According
to the EPA (Environmental Protection Agency) there have been over 900
million cell phones retired in the U.S. by 2007. Only about 5% of these are
recycled, with 75% being stored in people’s homes, and 20% going to
landfills or incinerators. It is estimated that over 165 million cell phones are
sold in the U.S. each year, and that number is increasing.
Organize the information in the paragraph above in the chart below:
Retired cell
phones by
2007
Percent
Recycled
Percent in
homes
Percent in
landfills or
incinerators
Cell phones
sold this year
in the U.S.
Using this information, answer the following questions. Show all
calculations.
1. How many cell phones in the U.S. had been recycled by 2007?
2. How many cell phones in the U.S. have been thrown away by 2007?
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3. If the average weight of a cell phone is 4 ounces, (2005 Nokia) how many
pounds of waste would be created by these cell phones being thrown away
in #2 above? (1 lb = 16 oz)
4. Of the cell phones sold in a year, how many would be recycled 18 months
later if the U.S. doubled its rate of recycling? (Use the original
percentages.)
5. Of the cell phones sold in a year, how many would be recycled if the cell
phones stored in people’s homes were added to those already being
recycled?
6. What would happen to the amount of e-waste from cell phones if the
average use time increased to 24 months? Explain.
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Cell Phone Pollution: Student
Worksheet
Teacher Key
Name:____________________________________ Class period:_________
Name: ______________________________
Class period:_________
While e-waste consists of discarded computers, cell phones, and other
electronic devices – let’s look at some data concerning cell phones in the
United States. Based upon a report by Inform, an environmental research
organization, the average cell phone is in use for only 18 months. According
to the EPA (Environmental Protection Agency) there have been over 900
million cell phones retired in the U.S. by 2007. Only about 5% of these are
recycled, with 75% being stored in people’s homes, and 20% going to
landfills or incinerators. It is estimated that over 165 million cell phones are
sold in the U.S. each year, and that number is increasing.
Organize the information in the paragraph above in the chart below:
Retired cell
phones by
2007
900,000,000
Percent
Recycled
Percent in
homes
5%
75%
Percent in
landfills or
incinerators
Cell phones
sold this year
in the U.S.
20%
165,000,000
Using this information, answer the following questions. Show all
calculations.
1. How many cell phones in the U.S. had been recycled by 2007?
900,000,000 x .05 = 45,000,000 recycled cell phones by 2007.
2. How many cell phones in the U.S. have been thrown away by 2007?
900,000,000 x .20 = 180,000,000 cell phones have been discarded by 2007.
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3. If the average weight of a cell phone is 4 ounces, how many pounds of
waste would be created by these cell phones being thrown away in #2
above? (1 lb = 16 oz)
180,000,000 x 4.0 oz = 720,000,000 oz
720,000,000 / 16 oz = 45,000,000 lbs of waste created by cell phones by
2007.
4. Of the cell phones sold in a year, how many would be recycled 18 months
later if the U.S. doubled its rate of recycling? (Use the original
percentages.)
165,000,000 x .1 = 16,500,000 cell phones would be recycled 18 months
after purchase.
5. Of the cell phones sold in a year, how many would be recycled if the cell
phones stored in people’s homes were added to those already being
recycled?
165,000,000 x (.05 + .75) = 132,000,000 cell phones would be recycled.
6. What would happen to the amount of e-waste from cell phones if the
average use time increased to 24 months? Explain.
The amount of e-waste would decrease because more people would be
holding on to their phones, and not disposing of them.
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Cell Phone Life Expectancy
Teacher Background Information: Cell phones
are a part of the lives of an ever-increasing
number of people all over the world. How long we
keep our old cell phone is a very important
decision with far reaching impacts.
Many things in nature can be shown to fit a
‘Normal Distribution’. Students should be familiar
with the characteristics of a normal distribution,
including the 68-95-99 shortcut, and how to use a
scientific calculator or computer to determine
probabilities associated with data in a normal
distribution.
Data source:
http://www.epa.gov/epaoswer/education/pdfs/lifecell.pdf
Goals: To use information about the life
expectancy of a cell phone to assess or review
properties of normally distributed data and to
determine the probabilities associated with such
data.
Objectives: Students will…


Content Area:
 Probability &
Statistics
 Normal distribution
curve
 finding probabilities
from normally
distributed data
Prerequisites:
 Understanding of
the properties and
uses of a normal
distribution curve
Standards met:
NM-DATA.9-12.3
NM-PROB.REA.PK-12.2
Time required:
20-30 minutes
Materials: (per student)
 Calculator (such as
a TI-83) or
computer capable
of statistical
analysis (normal
cumulative
distribution
function)needed:
Estimate probabilities associated with
normally distributed data using the 68-95-99
rule
Calculate probabilities of normally distributed
data, having different parameters, using available technology
(calculators or computers)
Procedure:
©2010 Beyond Benign – All Rights Reserved.

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To warm up ask students to define what the term life expectancy
means in terms of humans and in terms of electronics and appliances.
Ask students what factors may affect the life expectancy of electronics
and appliances.
Hand out the student worksheet.
Review details on the worksheet and answer any questions.
Give students time to complete the worksheet.
Review answers.
Hand out worksheet II and review and answer questions.
Review this whole series of lessons about cell phones and alert the
students to the following website http://recyclemycellphone.org .
explain that there are now places to recycle your cell phone but that
you have to be a savvy consumer as some recycling programs do not
match up to the idea of sustainability where economics, environment
and social equity are in harmony.
Have students read the article at the following web address:
http://www.greenpeace.org/international/campaigns/toxics/electronics
/where-does-e-waste-end-up
Ask students to write a paragraph evaluating e-waste issues against
the three E’s of sustainability (economics, environment and social
equity)
©2010 Beyond Benign – All Rights Reserved.
Cell Phone Life Expectancy: Student
Worksheet
Name:____________________________________ class period:_________
There are many things in nature that may be represented by a Normal
distribution. Let’s assume that the age at which cell phones are no longer in
use can be represented by a normal distribution, with a mean of 18 months.
You may remember that in a normal distribution, approximately 68% of the
data are within one standard deviation of the mean. (95% are within 2
standard deviations, and 99.7% are within 3 standard deviations of the
mean.) So, if we assume that 68% of the cell phones are used between 14
months and 22 months and then disposed of, then one standard deviation
would be about 4 months. (Normal distributions are symmetrical about the
mean.) Therefore we can write the following distribution statement: X ~
N(18,42) where X represents the age of cell phones at which they no longer
are in use. Using this distribution we can estimate the probability that a cell
phone will no longer be in use after a specific period of time. (i.e. P(X≤18)
= .5 or 50%)
Determine the following probabilities, using the 68-95-99 approximation
for the normally distributed data, rounding you answers to 3 decimal places
(the nearest tenth of a percent).
1. P(X≤14) = _________
2. P(X≤22) = _________
3. P(X≤26) = _________
4.P(10≤X≤18) = _________
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5. P(X>14) = _________
7. P(18≤X≤26) = _________
6. P(X>10) = _________
8. P(14≤X≤22) = _________
Now let’s look at the possible effect on such a distribution if everyone in the
U.S. kept using their old cell phone for a longer period of time, before they
got a new one. The average age of a cell phone would increase. Let’s
increase the mean to 24 months. Let’s also assume that 68% of the cell
phones are used between 18 and 30 months before they are taken out of
use. Therefore the standard deviation will be 6 months. Hence, X ~
N(24,62).
With the TI-83 graphing calculator, use the normal cumulative distribution
function [normalcdf(lower bound,upper bound,mean,standard
deviation] to determine the probabilities.
Using your calculator/computer, determine the following probabilities,
rounding you answers to 3 decimal places (the nearest tenth of a percent).
1. P(X≤14) = _________
2. P(X≤22) = _________
3. P(X≤26) = _________
4.P(10≤X≤18) = _________
5. P(X>14) = _________
6. P(X>10) = _________
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7. P(18≤X≤26) = _________
8. P(14≤X≤22) = _________
With technology improving at an ever-increasing rate, and Americans not
wanting to be left behind, it is more likely that the average age of a cell
phone remaining in use will decrease. If this should happen, how do you
expect the probabilities that you calculated above will change? Make a
prediction, or explain why you cannot.
Now, calculate the following probabilities using the following distribution: X
~ N(12,2.52)
(Again, round you answers to 3 decimal places or the nearest tenth of a
percent.)
1. P(X≤14) = _________
2. P(X≤22) = _________
3. P(X≤26) = _________
4.P(10≤X≤18) = _________
5. P(X>14) = _________
6. P(X>10) = _________
7. P(18≤X≤26) = _________
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8. P(14≤X≤22) = _________
Explain how these results prove, or disprove, your prediction.
If our goal, as a society, is to create less waste and to conserve more
natural resources, what direction concerning cell phone use should we
travel?
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Cell Phone Life Expectancy: Student
Worksheet
Teacher Key
Name:____________________________________ class period:_________
There are many things in nature that may be represented by a Normal
distribution. Let’s assume that the age at which cell phones are no longer in
use can be represented by a normal distribution, with a mean of 18 months.
You may remember that in a normal distribution, approximately 68% of the
data are within one standard deviation of the mean. (95% are within 2
standard deviations, and 99.7% are within 3 standard deviations of the
mean.) So, if we assume that 68% of the cell phones are used between 14
months and 22 months and then disposed of, then one standard deviation
would be about 4 months. (Normal distributions are symmetrical about the
mean.) Therefore we can write the following distribution statement: X ~
N(18,42) where X represents the age of cell phones at which they no longer
are in use. Using this distribution we can estimate the probability that a cell
phone will no longer be in use after a specific period of time. (i.e. P(X≤18)
= .5 or 50%)
Determine the following probabilities, using the 68-95-99 approximation
for the normally distributed data, rounding you answers to 3 decimal places
(the nearest tenth of a percent).
1. P(X≤14) = __16%__
1 – (.50 + .68/2)
3. P(X≤26) = __97.5%_
.50 + .95/2
5. P(X>14) = __84%__
.50 + .68/2
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2. P(X≤22) = __84%__
.50 + .68/2
4.P(10≤X≤18) = __47.5%__
.95/2
6. P(X>10) = __97.5%__
.50 + .95/2
7. P(18≤X≤26) = __47.5%__
.95/2
8. P(14≤X≤22) = __68%__
.68
Now let’s look at the possible effect on such a distribution if everyone in the
U.S. kept using their old cell phone for a longer period of time, before they
got a new one. The average age of a cell phone would increase. Let’s
increase the mean to 24 months. Let’s also assume that 68% of the cell
phones are used between 18 and 30 months before they are taken out of
use. Therefore the standard deviation will be 6 months. Hence, X ~
N(24,62).
With the TI-83 graphing calculator, use the normal cumulative distribution
function [normalcdf(lower bound,upper bound,mean,standard
deviation] to determine the probabilities.
Using your calculator/computer, determine the following probabilities,
rounding you answers to 3 decimal places (the nearest tenth of a percent).
1. P(X≤14) = __4.8%___
2. P(X≤22) = __36.9%__
Normalcdf(-10,14,24,6)
Normalcdf(-10,22,24,6)
3. P(X≤26) = __63.1%__
4.P(10≤X≤18) = __14.9%__
Normalcdf(-10,26,24,6)
Normalcdf(10,18,24,6)
5. P(X>14) = __95.2%__
6. P(X>10) = __99.0%__
Normalcdf(14,50,24,6)
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Normalcdf(10,50,24,6)
7. P(18≤X≤26) = __47.2%__
Normalcdf(18,26,24,6)
8. P(14≤X≤22) =__32.2%__
Normalcdf(14,22,24,6)
With technology improving at an ever increasing rate, and Americans not
wanting to be left behind, it is more likely that the average age of a cell
phone remaining in use will decrease. If this should happen, how do you
expect the probabilities that you calculated above will change? Make a
prediction, or explain why you cannot.
Answers may vary. Students should discuss the shift in the normal curve
and the area associated with that shift.
Now, calculate the following probabilities using the following distribution: X
~ N(12,2.52)
(Again, round you answers to 3 decimal places or the nearest tenth of a
percent.)
1. P(X≤14) = __78.8%__
2. P(X≤22) = __100%__
Normalcdf(-10,14,12,2.5)
Normalcdf(-10,22,12,2.5)
3. P(X≤26) = __100%__
4.P(10≤X≤18) = __78.0%__
Normalcdf(-10,26, 12,2.5)
Normalcdf(10,18, 12,2.5)
5. P(X>14) = __21.2%__
6. P(X>10) = __78.8%__
Normalcdf(14,50,12,2.5)
Normalcdf(10,50, 12,2.5)
7. P(18≤X≤26) = __0.8%__
Normalcdf(18,26, 12,2.5)
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8. P(14≤X≤22) = __21.2%__
Normalcdf(14,22,12,2.5)
Explain how these results prove, or disprove, your prediction.
Answers will vary.
If our goal, as a society, is to create less waste and to conserve more
natural resources, what direction concerning cell phone use should we
travel?
Answers will vary. Students should mention keeping cell phones longer,
and/or recycling older cell phones.
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Cell Phone Life Expectancy: Student
Worksheet II
Name:____________________________________ Class period:_________
Using the idea that the age of a cell phone (the time it is used before being
discarded/recycle) is normally distributed, with a mean of 18 months and a
standard deviation of 4 months, we can state: X ~ N(18,42)
Based upon information from the EPA, there are approximately 135 million
cell phones sold in the U.S. each year. Using the proportions associated
with this normally distributed data, answer the following questions (showing
your math to support each answer). Using your calculator/computer, round
you answers to 3 decimal places or the nearest thousand cell phones.
1. How many of the 135 million cell phones sold this year will no longer be in
use . . .
a. 12 months from now?
b. 24 months from now?
c. 30 months from now?
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2. How many of the 135 million cell phones sold this year will still be in use ?
a. 6 months from now?
b. 15 months from now?
c. 2 years from now?
3. If 5% of the cell phones that are no longer in use are recycled, how many
of these 135 million cell phones sold this year will be recycled in one year
from now?
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Cell Phone Life Expectancy: Student
Worksheet II - Teacher Key
Name:____________________________________ Class period:_________
Using the idea that the age of a cell phone (the time it is used before being
discarded/recycle) is normally distributed, with a mean of 18 months and a
standard deviation of 4 months, we can state: X ~ N(18,42)
Based upon information from the EPA, there are approximately 135 million
cell phones sold in the U.S. each year. Using the proportions associated
with this normally distributed data, answer the following questions (showing
your math to support each answer). Using your calculator/computer, round
you answers to the nearest whole cell phone.
1. How many of the 135 million cell phones sold this year will no longer be in
use . . .
a. 12 months from now?
135,000,000 x P(X ≤ 12)
135,000,000 x [normalcdf(-10,12,18,4)] ≈ 9,018,976 cell phones
b. 24 months from now?
135,000,000 x P(X ≤ 12)
135,000,000 x [normalcdf(-10,24,18,4)] ≈ 125,981,024 cell phones
c. 30 months from now?
135,000,000 x P(X ≤ 12)
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135,000,000 x [normalcdf(-10,30,18,4)] ≈ 134,817,754 cell phones
2. How many of the 135 million cell phones sold this year will still be in use .
..
a. 6 months from now?
135,000,000 x P(X ≥ 6)
135,000,000 x [normalcdf(6,50,18,4)] ≈ 134,817,754 cell phones
b. 15 months from now?
135,000,000 x P(X ≥ 15)
135,000,000 x [normalcdf(15,50,18,4)] ≈ 104,405,317 cell phones
c. 2 years from now?
135,000,000 x P(X ≥ 24)
135,000,000 x [normalcdf(24,50,18,4)] ≈ 9,018,976 cell phones
3. If 5% of the cell phones that are no longer in use are recycled, how many
of these 135 million cell phones sold this year will be recycled in one year
from now?
135,000,000 x 5% x P(X ≤ 12)
135,000,000 x .05 x [normalcdf(-10,12,18,4)] ≈ 450,949 cell phones
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Where does e-waste end up? – By Greenpeace
Many old electronic goods gather dust
in storage waiting to be reused,
recycled or thrown away. The US
Environmental Protection Agency
(EPA) estimates that as much as three
quarters of the computers sold in the
US are stockpiled in garages and
closets. When thrown away, they end
up in landfills or incinerators or, more
recently, are exported to Asia.
Landfill: According to the US EPA, more than 4.6 million tonnes of e-waste
ended up in US landfills in 2000. Toxic chemicals in electronics products can
leach into the land over time or are released into the atmosphere, impacting
nearby communities and the environment. In many European countries,
regulations have been introduced to prevent electronic waste being dumped
in landfills due to its hazardous content. However, the practice still continues
in many countries. In Hong Kong for example, it is estimated that 10-20
percent of discarded computers go to landfill.
Incineration: This releases heavy metals such as lead, cadmium and
mercury into the air and ashes. Mercury released into the atmosphere can
bioaccumulate in the food chain, particularly in fish - the major route of
exposure for the general public. If the products contain PVC plastic, highly
toxic dioxins and furans are also released. Brominated flame retardants
generate brominated dioxins and furans when e-waste is burned.
Reuse: A good way to increase a product's lifespan. Many old products are
exported to developing countries. Although the benefits of reusing
electronics in this way are clear, the practice is causing serious problems
because the old products are dumped after a short period of use in areas
that are unlikely to have hazardous waste facilities.
Recycle: Although recycling can be a good way to reuse the raw materials
in a product, the hazardous chemicals in e-waste mean that electronics can
harm workers in the recycling yards, as well as their neighbouring
communities and environment.
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In developed countries, electronics recycling takes place in purpose-built
recycling plants under controlled conditions. In many EU states for example,
plastics from e-waste are not recycled to avoid brominated furans and
dioxins being released into the atmosphere. In developing countries
however, there are no such controls. Recycling is done by hand in scrap
yards, often by children.
Export: E-waste is routinely exported by developed countries to developing
ones, often in violation of the international law. Inspections of 18 European
seaports in 2005 found as much as 47 percent of waste destined for export,
including e-waste, was illegal. In the UK alone, at least 23,000 metric tonnes
of undeclared or 'grey' market electronic waste was illegally shipped in 2003
to the Far East, India, Africa and China. In the US, it is estimated that 50-80
percent of the waste collected for recycling is being exported in this way.
This practice is legal because the US has not ratified the Basel Convention.
Mainland China tried to prevent this trade by banning the import of e-waste
in 2000. However, we have discovered that the laws are not working; ewaste is still arriving in Guiya of Guangdong Province, the main centre of ewaste scrapping in China.
We have also found a growing e-waste trade problem in India. 25,000
workers are employed at scrap yards in Delhi alone, where 10-20000 tonnes
of e-waste is handled each year, 25 percent of this being computers. Other
e-waste scrap yards have been found in Meerut, Ferozabad, Chennai,
Bangalore and Mumbai.
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© UNEP
How did the trade evolve?
In the 1990s, governments in the EU, Japan and some US states set up ewaste 'recycling' systems. But many countries did not have the capacity to
deal with the sheer quantity of e-waste they generated or with its hazardous
nature.
Therefore, they began exporting the problem to developing countries where
laws to protect workers and the environment are inadequate or not
enforced. It is also cheaper to 'recycle' waste in developing countries; the
cost of glass-to-glass recycling of computer monitors in the US is ten times
more than in China.
Demand in Asia for electronic waste began to grow when scrap yards found
they could extract valuable substances such as copper, iron, silicon, nickel
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and gold, during the recycling process. A mobile phone, for example, is 19
percent copper and eight percent iron.
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