Homework Answers
11.1 p. 747-48: 3, 7, 8, 9, 10, 11-21(odd), 28
8. 6
28. mean: 110, median: 112, mode: 114, range:
23, std. dev.: 6.5
Chapter 11 Timeline
My website:
http://teacher.edmonds.wednet.edu/edmondswoodway/yshadyry
a/index.php
Fri 13:
• 11. 1 p. 747-48: 3, 7, 8, 9, 10, 11-21(odd), 28
Wed 18/Thur 19: 11.2 – 11.3
• 11.2 p. 753-55: 1-17 (every other odd), 19, 23.
• 11.3 p. 760-61: 3, 7, 9, 11-15 (odd), 17-33 (every other odd).
Mon 23/Tue 24: Chapter Review (p. 784-785), Chapter Test(p.
787)
Wed 25/Thur 26: Chapter 11 Test
11.2 Apply Transformations to Data
Warm-up(10 min): In your groups(of 3-4)
1. Find mean, median, mode, range and
standard deviation of the following data set:
7, 12, 16, 20, 20
2. Add 10 to every data value and find all of the
measures above for the new data set.
3. Compare results for both data sets. What can
you conclude?
Adding a constant to all data values
• Increases the measures of central tendency by
the same constant
• Does not change the measures of dispersion.
Try this:
Below are the measures of central tendencies and
dispersion of the data set is comprised of the weights of 8
astronauts without their suits on. What are the mean,
median, mode, range, and std.dev., when all astronauts
are wearing their suits (a suit weights 250lb)?
Multiplying data values by a constant multiplies
the measures of central tendency and dispersion
by the same constant.
Multiply data values by a constant
Example 2 (p. 752):
Below are the measures of central tendencies and dispersion
of the data set is comprised of the winning distances (in
meters) in the men’s Olympic triple jump events from 1964 to
2004. What are the mean, median, mode, range, and std.dev.,
when all the distances are in feet? (1 meter = 3.28 feet)
11.3 Use Normal Distributions
A normal distribution is a type of probability
distribution. It is modeled by a bell-shaped
curve called a normal curve that is symmetric
about the mean.
Areas Under a Normal Curve
Find a normal probability
Example 1(p. 757) Find P(x – 2σ ≤ x ≤ x) of an xvalue randomly selected from the distribution.
P(x – 2σ ≤ x ≤ x) = 0.135 + 0.34 = 0.475
Interpret normally-distributed data
Example 2 (p. 758): The blood cholesterol readings for a group of women are normally
distributed with a mean of 172 mg/dl and a standard deviation of 14 mg/dl.
a. About what percent of the women have readings between 158 and 186?
How many standard deviations are these readings from the mean?
Look at the normal curve again…
68%
b. About what percent of the readings are higher than 200?
2.5%
Standard Normal Distribution
Mean: 0
Standard Deviation: 1
𝑥−𝑥
𝑧 − 𝑠𝑐𝑜𝑟𝑒: 𝑧 =
σ
Standard Normal Table
Use a z-score
Example 3 (p. 759) Scientists conducted aerial
surveys of a seal sanctuary and recorded the
number x of seals they observed during each
survey. Mean: 73. Standard Deviation: 14.1.
Find the probability that at most 50 seals were
observed during a survey.
Step 1: Find the z-score:
𝑥 − 𝑥 50 − 73
𝑧=
=
≈ −1.6
𝜎
14.1
Step 2: use the Standard Normal Table to find
P(x ≤ 50) ≈ P(z ≤ -1.6) = 0.0548
Homework
• 11.2 p. 753-55: 1-17 (every other odd), 19, 23.
• 11.3 p. 760-61: 3, 7, 9, 11-15 (odd), 17-33
(every other odd).