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AP Statistics
Module 1 Review
1.
Suppose the weight of household cats is normally distributed with a mean of 12 pounds and a standard
deviation of 2.5 pounds. A cat is considered overweight if it weighs more than 18 pounds.
a. What proportion of cats are considered overweight?
b. What proportion weigh less than 10.7 pounds?
c. What proportion weigh between 9.8 and 15 pounds?
2.
A density curve is made from a line segment extending from the point (0, ½) to the point (2, ½). What percent
of the observations are between 0.3 and 1.7?
3.
Consider a normal distribution where 95% of the observations are between 10 and 17. What is an estimate of
the standard deviation of this distribution?
4.
The heights of adult giraffes is normally distributed with a mean of 18 feet.
a. If 20% of giraffes are taller than 19.5 feet, what is the standard deviation?
b. If 15% of giraffes are shorter than 16 feet, what is the standard deviation?
5. The following are the winning scores of each of the Super Bowls in history. Do these data appear to follow a
normal distribution? Explain your answer. Include a sketch of the normal probability plot.
17
52
27
29
37
32
21
20
21
24
55
16
32
20
24
48
42
14
20
39
24
34
46
16
23
38
23
34
38
16
31
27
33
35
26
35
27
27
49
31
30
35
6.
Suppose your data give you the following 5 number summary: 3, 7, 15, 23, 37. If there are 500 pieces of data
and the data is approximately normal, find the variance.
7.
The amount of cash (rounded to the nearest dollar) found in the wallets of 12 teens at the mall is given in the
stemplot below. Find the median and mean of the data set.
0:3 8
1:0 5 8
2:2 7 9
3:0 4
4:1
5:8
8.
Based on the histogram below, what can you say about the mean and the median? Explain your answer.
9.
Give an example of a data set whose standard deviation is 0.
10. Your pediatrician said that you are in the 30th percentile for height. What does that mean?
11. Explain how a normal probability plot can help you assess normality.
12. You just discovered the random number generator on your calculator. How fun! You can generate any number
(decimals, too) in a given range. You and a friend pay a game where you have the calculator generate a number
between 0 and 650 (inclusive). You win if the number is between 200 and 400. What is the probability that you
win this game?
13. Suppose you measured the weights of members of a population and found the weights to be normally
distributed. The distribution has a mean weight of 160 pounds and a standard deviation of 25 pounds. What
weight is associated with the 70th percentile?
14. A used car lot is having a slow month. The manager decides to slash prices by lowering the price of every car on
the lot by $1000. How will this affect the mean, median, standard deviation, and interquartile range of the car
prices?
15. Find the 20th and 85th percentiles of the standard normal distribution.
16. An article on peanut butter in Consumer Reports (September 1990) reported the following scores (quality
ratings on a scale of 0 to 100) for various brands:
Creamy: 56
40
22
44
56
62
68
36
41
39
30
53
40
50
50
65
56
45
30
Crunchy: 62
50
53
34
75
42
42
36
47
75
40
80
34
47
62
56
52
99
(a) Are there any outliers in either of the two data sets? Justify your answer numerically.
(b) Compare the distributions of quality ratings for the different types of peanut butter.
17. Below is a histogram representing weights of book bags of high school students. (I know, I know…I made that up.
But, you get the idea! )
a) Describe the shape of the distribution.
b) A local Apple dealer wants schools to encourage schools to issue iPads and have students use eBooks instead
of carrying around bulky textbooks. Which measure of center should the Apple dealer use to report that overall book
bag weight is high? Explain.