# AP stats Chapter 2 Practice Test 2017

```AP stats Chapter 2 Practice Test
Modeling distributions of data
Name ______________________________
Per ___ Date ________________________
According to the National Center for Health Statistics, the distribution of heights for 15-year old males is
symmetric, single-peaked, and bell shaped. For this distribution, a z-score of 0 corresponds to a height of 170
centimeters and a z-score of 1 corresponds to a height of 177.5 centimeters.
_____ 1.) What is the mean and standard deviation of the data?
a.) Mean = 170cm, standard deviation = 177.5cm
b.) Mean = 177.5 cm, standard deviation = 170 cm
c.) Mean = 170cm, standard deviation = 7.5 cm
d.) Mean = 7.5cm, standard deviation = 177.5 cm
e.) Mean = 0, standard deviation = 1
_____ 2.) What height would correspond to a z-score of 2.5?
a.) 188.75 cm
b.) 151.25 cm
c.) 196.25 cm
e.) None of the above is correct
d.) 158.75 cm
_____ 3.) Only 5% of 15-year old males have heights outside of the range of
a.) 162.5cm to 177.5cm
b.) 155cm to 185cm
c.) 147.5cm to 192.5 cm
d.) 170cm to 185cm
e.) None of the above is correct
_____ 4.) What percent of 15-year old males are over 185cm tall?
a.) 95%
b.) 5%
c.) 97.5%
d.) 2.5%
e.) 68%
Use a standard normal distribution to answer the questions
_____ 5.) The proportion of scores that are less than 1.25 is closest to
a.) 0.8944
b.) 0.1056
c.) 0.5987
d.) 0.4013
e.) None of the above
_____ 6.) The proportion of scores that are greater than -1.45 is closest to
a.) 0.6736
b.) 0.3264
c.) 0.0735
d.) 0.9265
e.) None of the above
_____ 7.) The percent of scores that fall between -1.45 and 1.25 is closest to
a.) 10.56
b.) 7.35
c.) 89.47
d.) 32.64
e.) 82.08
List all statements that apply to each density graph: Normal, right-skewed, left-skewed, symmetric, area under
the curve is 1, mean is greater than median, median is greater than mean, mean and median are equal.
8.)
9.)
10.)
11.)
_____ 12. The graph to the right is a Normal Probability Plot for the raw scores
on the chapter 1 test. Which of the statements is true about the shape of the
test scores?
a.) The distribution is approximately normal
b.) The distribution is skewed left
c.) The distribution is skewed right
d.) There are no outliers
e.) There is insufficient information to determine the shape of the distribution
_____ 13.) The graph to the right is a Normal Probability Plot for the raw scores
on the chapter 1 test. Which of the statements is true about the shape of the
test scores?
a.) The distribution is approximately normal
b.) The distribution is skewed left
c.) The distribution is skewed right
d.) There are no outliers
e.) There is insufficient information to determine the shape of the distribution
The cumulative relative frequency graph at the left shows the
distribution of how long it takes a vehicle to stop after pressing on the
breaks at a certain speed.
_____ 14.) The interquartile range for the distribution is
a.) 12
b.) 20
c.) 32
d.) 8
e.) 25
_____ 15.) Approximately what proportion of the cars stopped in more
than 10 seconds?
a.) 0.85
b.) 0.15
c.) 0.30
d.) 0.70
e.) 25
_____ 16.) A group of Australian students were asked to estimate the width of their classroom in feet. The
mean was 43.7ft, the standard deviation was 12.5ft, and the distribution was skewed right. The distribution of
their z-scores for the width is
a.) Normally distributed with a mean of 43.7 and a standard deviation of 12.5
b.) Skewed left with a mean of 43.7 and a standard deviation of 12.5
c.) Skewed right with a mean of 43.7 and a standard deviation of 12.5
d.) Normally distributed with a mean of 0 and a standard deviation of 1
e.) Skewed right with a mean of 0 and a standard deviation of 1
_____ 17.) If a distribution is symmetrical, which of the following is true?
(a) The mean must be less than the median.
(b) The mean and median must be equal.
(c) The mean must be greater than the median.
(d) The mean is either equal to or less than the median,
(e) It’s impossible to tell which of the above statements is true without seeing the data.
_____ 18.) If a distribution is skewed to the right, which of the following is true?
(a) The mean must be less than the median.
(b) The mean and median must be equal.
(c) The mean must be greater than the median.
(d) The mean is either equal to or less than the median,
(e) It’s impossible to tell which of the above statements is true without seeing the data.
_____ 19.) If a distribution is skewed to the left, which of the following is true?
(a) The mean must be less than the median.
(b) The mean and median must be equal.
(c) The mean must be greater than the median.
(d) The mean is either equal to or less than the median,
(e) It’s impossible to tell which of the above statements is true without seeing the data.
_____ 20.) The mean mercury concentration in sampled cans of tuna is 0.285 ppm with a standard deviation
of 0.300ppm. Which of the following is a correct interpretation of standard deviation?
(a) The mean amount of mercury in all other cans of tuna will be within 0.300 ppm of the mean.
(b) All cans of tuna have between 0 and 0.585 ppm of mercury in them.
(c) About half the cans of tuna have between 0 and 0.585 ppm of mercury in them
(d) The difference in the mean and the median amount of mercury is 0.300 ppm
(e) The distance between the ppm of mercury in each can and the mean ppm is, on average, about
0.300ppm
_____ 21.) A survey was designed to study how business operations vary according to their size. Companies
were classified as small, medium, or large. Questionnaires were sent to 200 randomly selected
businesses of each size. Since not all questionnaires in a survey of this type are returned ,
researchers decided to investigate the relationship between the response rate and the size of the
business. The data is shown in the table below:
Size
Response No Response
Total
Small
125
75
200
Medium
81
119
200
Large
40
160
200
Which of the following conclusions seems to be supported by the data?
(a) There are more small companies than large companies in the survey.
(b) Small companies appear to have a higher response rate than medium or big companies.
(c) Exactly the same number of companies responded as didn’t respond.
(d) Small companies dislike larger companies
(e) If we combine the medium and large companies, then their response rate would be equal to that of
the small companies.
_____ 22. If a distribution is symmetrical, which of the following is true?
(a) The mean must be less than the median.
(b) The mean and median must be equal.
(c) The mean must be greater than the median.
(d) The mean is either equal to or less than the median,
(e) It’s impossible to tell which of the above statements is true without seeing the data.
_____ 23. If a distribution is skewed to the right, which of the following is true?
(a) The mean must be less than the median.
(b) The mean and median must be equal.
(c) The mean must be greater than the median.
(d) The mean is either equal to or less than the median,
(e) It’s impossible to tell which of the above statements is true without seeing the data.
_____ 24. If a distribution is skewed to the left, which of the following is true?
(a) The mean must be less than the median.
(b) The mean and median must be equal.
(c) The mean must be greater than the median.
(d) The mean is either equal to or less than the median,
(e) It’s impossible to tell which of the above statements is true without seeing the data.
25.) The Presidential Physical Fitness Program gives awards to those who meet qualifying standards in five
events. The standards are based on the 1985 School Population Fitness Survey. For the National Award, the
standard is the 50th percentile for a specific age group and gender.
Jane, who is 9 years old, did 40 curl-ups in one minute. Matt, who is 12 years old, also did 40 curl-ups
in one minute. The standard for the National Award are 30 curl-ups for Jane and 35 curl-ups for Matt. The
standard deviation is 10 and 8 curl-ups respectively. The distributions are approximately normal.
a.) How do Jane’s and Matt’s performances compare? Provide appropriate statistical calculations to
b.) Estimate the number of 9-year old girls that could do more than 40 curl-ups, if 250 girls participated in
the program.
c.) Estimate the 90th percentile for 12-year old boys.
26.) Rainwater was collected in water collectors at 30 different sites near an industrial complex, and the
amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and
1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error.
The error can be corrected by adding 0.1 pH units to all of the values and then multiplying the result by 1.2.
What is the new mean and standard deviation? Show all your work and explain your reasoning.
27.) Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For
Math scores, the mean under the old scale was 470 and the standard deviation was 110. In 2009, the
mean was 515 and the standard deviation was 116.
a.) What is the standardized score for a student who scored 500 on the old scale?
b.) Jane took the SAT in 1994 and scored 500. Colleen took the SAT in 2009 and scored 530. Compare
c.) The distributions for the tests are approximately normal. Find the 75th percentile for both tests.
d.) The distributions for the tests are approximately normal. What percentage of students scored above
800 on both tests?
28.) Does party affiliation differ among the genders? A review of voter registration in a small town yielded
the following table of the number of males and females registered for each party
Party Affiliation
Democrat
Republican
Other
Total
Male
300
500
200
1000
Female
600
300
100
1000
Total
900
800
300
2000
a.) Calculate the conditional distributions for party affiliation among each gender. You may present your
results in either a table or a graph.
b.) Discuss the relationship between gender and party affiliation in two or three sentences.
```