Statistics 101L – Homework 3
Solution
Assignment:
Weights of adult males and females have increased over the past 40 years but so have
heights. The body mass index (BMI) combines information about an individual’s height
and weight and can be used to classify individuals into a Weight Status category.
BMI
Below 18.5
18.5  BMI  25.0
25.0  BMI  30.0
30.0 and above
Weight Status
Underweight
Normal weight
Overweight
Obese
Below is information on BMI for males and females age 18 and 19 in 1980, 1990 and
2000.
BMI
mean, μ
std. dev., σ
1980
males
females
22.8
22.4
4.4
4.4
1990
males
females
23.1
23.3
5.2
5.4
2000
males
females
24.5
24.9
5.9
6.0
1. Use the 68-95-99.7 rule to find …
a) the percentage of males in 1980 with BMI less than 14.0.
2.5%
95% of BMIs will be between 14.0 and 31.6, therefore
2.5% will be less than 14.0.
b) the percentage of females in 1980 with BMI greater than 18.0.
84%
68% of BMIs will be between 18.0 and 26.8, therefore
68 + 16 = 84% will be greater than 18.0.
c) the BMI values that correspond to the central 95% of the distribution of
males in 2000?
24.5 – 2(5.9) = 12.7 to 24.5 + 2(5.9) = 36.3
d) the value such that 0.15% of females in 2000 have BMIs greater than the
value.
42.9
99.7% of BMI values will be between 6.9 and 42.9,
therefore 0.15% will be greater than 42.9.
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2. Use Table Z in the text to answer the following questions about 18 and 19 year
olds.
a) What percentage of females in 1980 would be classified as underweight?
18.7%
18.5  22.4  3.9

 0.89
4.4
4.4
0.1867
z
b) What percentage of females in 1990 would be classified as underweight?
18.7%
18.5  23.3  4.8

 0.89
5.4
5.4
0.1867
z
c) What percentage of females in 2000 would be classified as underweight?
14.2%
18.5  24.9  6.4

 1.07
5.9
6.0
0.1423
z
d) Comment on the change from 1980 to 2000 in the percentages of females
classified as underweight.
The percentage underweight females stayed the same between 1980
and 1990 and then dropped in 2000.
e) What percentage of males in 1980 would be classified as obese?
5.1%
30  22.8 7.2

 1.64
4.4
4.4
1  0.9495  0.0505
z
f) What percentage of males in 1990 would be classified as obese?
9.2%
30  23.1 6.9

 1.33
5.2
5.2
1  0.9082  0.0918
z
g) What percentage of males in 2000 would be classified as obese?
17.6%
30  24.5 5.5

 0.93
5.9
5.9
1  0.8238  0.1762
z
2
h) Comment on the change from 1980 to 2000 in the percentages of males
classified as obese.
The percentage of obese males has increased, almost doubling every
10 years.
i) We wish to identify the cutoff value in 2000 such that 15% of the
population has BMI greater than this cutoff. Find the cutoff value for
males and the cutoff value for females.
15%  z  1.04
15%  z  1.04
cutoff males  24.5  1.04( 5.9 )
cutoff females  24.9  1.04( 6.0 )
cutoff males  24.5  6.136
cutoff females  24.9  6.24
cutoff males  30.64
cutoff females  31.14
3. Use the JAVA applet found on the web to answer the following questions. Some
sites are:
http://davidmlane.com/hyperstat/z_table.html
a) What percentage of males in 1980 would be classified as overweight?
0.2576561 or 25.8%
b) What percentage of males in 1990 would be classified as overweight?
0.265145 or 26.5%
c) What percentage of males in 2000 would be classified as overweight?
0.290616 or 29.1%
d) What percentage of females in 1980 would be classified as normal
weight?
0.534999 or 53.5%
e) What percentage of females in 1980 would be classified as normal
weight?
0.436517 or 43.7%
f) What percentage of females in 2000 would be classified as normal
weight?
0.363588 or 36.4%
g) We want to make a new weight status category that identifies the 2% of
females in 2000 with the highest BMIs. What BMIs should be included in
this new category?
above 37.2225
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h) Repeat part g) but this time for males.
above 36.6171
4. Stat 101 students in the past answered questions on a Stat 101 Survey at the
beginning of the semester. The anonymous responses are in the JMP data table
StatSurvey.JMP on the course web page.
a) Go to the Stat 101 course webpage and open the StatSurvey file.
b) Go to the Tables pull-down menu and select Subset. Click on the circle
next to Random Sample and enter 50 in the box for Sampling Ratio or
Sample Size. Click on OK. This will create a new JMP data table
consisting of a random selection of 50 cases from the StatSurvey. Use this
new JMP data table for parts c) and d).
Each student will have a different random selection and so you should
compare the student’s description against the JMP output. Below is a
sample description.
c) Use Analyze – Distribution to create a Histogram, Box plot and Normal
Quantile Plot for the variable height. Describe each of the plots and use
your descriptions to comment on whether the random sample of heights
could have come from a population with a distribution that follows a
normal model. Turn in the JMP output with your assignment.
Histogram: Bi-modal (some samples will give a symmetric mounded
in the middle shape). The center is around 67.5 inches with values
spread from 58 to 77 inches.
Box plot: Fairly symmetric (note that the mean and median are fairly
close) with no apparent outliers.
Normal Quantile Plot: The heights generally follow the straight line
that indicates a normal distribution. There is no apparent curvature
in the plot.
The sample could have come from a population whose distribution
follows a normal model.
Note: Even with the bi-modal shape in the histogram, the box plot and
the normal quantile plot indicate the sample could have come from a
normal distribution. For some random samples the bi-modal shape in
the histogram may show up in the normal quantile plot. Students
may then conclude that the sample did not come from a population
whose distribution follows a normal model.
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d) Use Analyze – Distribution to create a Histogram, Box plot and Normal
Quantile Plot for the variable musiccds. Describe each of the plots and
use your descriptions to comment on whether the random sample of
heights could have come from a population with a distribution that follows
a normal model. Turn in the JMP output with your assignment.
Histogram: Mounded on the left and skewed to the right. The center
is around 100 with values spread from 0 to 1000.
Box plot: Skewed right (note that the mean is much larger than the
median) with several potential outliers, values above 250.
Normal Quantile Plot: The number of music cds start out following
straight line but not the one that indicates a normal distribution.
There is a considerable amount of curvature in the plot.
The sample probably did not come from a population whose
distribution follows a normal model. The population distribution is
most likely skewed right.
5
3
.99
2
.95
.90
.75
.50
1
0
.25
.10
.05
.01
Normal Quantile Plot
Distribution: height
-1
-2
-3
10
Count
15
5
55
60
65
70
75
80
Quantiles
100.0%
75.0%
50.0%
25.0%
0.0%
Moments
Mean
Std Dev
N
maximum
quartile
median
quartile
minimum
77.000
70.250
67.500
65.000
58.000
67.56
3.8869746
50
6
3
.99
2
.95
.90
.75
.50
1
0
.25
.10
.05
.01
Normal Quantile Plot
Distribution: musiccds
-1
-2
-3
40
20
Count
30
10
0
200
400
600
800
1000 1200
Quantiles
100.0%
75.0%
50.0%
25.0%
0.0%
Moments
Mean
Std Dev
N
maximum
quartile
median
quartile
minimum
1000.0
105.0
55.0
20.0
0.0
113.4
177.83838
50
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