AP Statistics
Chapter 9 Exercises
Mr. Dooley
NAME____________________________________
Section 9-1
In the first 6 exercises, state (a) whether each boldface number is a parameter or a statistic and (b) use
appropriate notation to describe each number.
1.) The Tennessee STAR experiment randomly assigned children to regular or small classes during their
first four years of school. When these children reached high school, 40.2% of blacks from small classes
took the AT or SAT college entrance exam. Only 31.7% of blacks from regular classes took one of these
exams.
2.) A random sample of female college students has a mean height of 64.5 inches, which is greater than
the 63 inch mean height of all adult American women.
3.) The ball bearings in a large container have mean diameter 2.5003 centimeters. This is within the
specifications for acceptance of the container by the purchaser. By chance, an inspector chooses 100
bearings from the container that have a mean diameter of 2.5009 centimeters. Because this is outside the
specified limits, the container is mistakenly rejected.
4.) The Bureau of Labor Statistics last month interviewed 60,000 members of the US labor force, of
whom 7.2% were unemployed.
5.) A telemarketing firm in L.A. uses a device that dials residential phone numbers in Los Angeles at
random. Of the first 100 numbers dialed, 48% are unlisted. This is not surprising, because 52% of all
L.A. phone numbers are unlisted.
6.) A researcher carries out a randomized comparative experiment with young rats to investigate the
effects of a toxic compound in food. She feeds the control group a normal diet. The experimental group
receives a diet with 2500 part per million of the toxic material. After 8 weeks, the mean weight gain is
335 grams for the control group and 289 grams for the experimental group.
Ronald scores 700 on the math section of the SAT exam. The distribution of SAT scores is
approximately normal with a mean of 500 and a standard deviation of 100. Jeff takes the ACT math exam
and scores a 31. ACT scores are approximately normally distributed with a mean of 18 and a standard
deviation of 6.
7.) Relative to their peers who also took the tests, who performed better on his test? Explain
8.) A certain college will only consider those students in the top 1% in the math section. What grades do
Ronald and Jeff have to receive on their respective tests in order to be considered for admission? Show
your work below.
9.) Between what two grades does 95% of the population fall for the ACT and SAT exams? Show your
work below.
Section 9-2
10.) Voter registration records show that 68% of all voters in Indianapolis are registered as Republicans.
To test whether the numbers dialed by a random digit dialing service device really are random. You use
the device to call 150 randomly chosen residential telephones in Indianapolis. Of the registered voters
contacted, 73% are registered Republicans.
a.) Is 68% a parameter or a statistic? Give the appropriate notation
b.) Is 73% a parameter or a statistic? Give the appropriate notation
c.) What are the mean and standard deviation of the sample proportion of registered Republicans in
samples of size 150 from Indianapolis?
d.) Find the probability of obtaining an SRS of size 150 from the population of Indianapolis voters in
which 73% or more are registered Republicans. How well is your random digit device working?
11.) Explain why you cannot use the methods from this chapter to find the following probabilities.
a.) A factory employs 3000 unionized workers, of whom 30% are Hispanic. The 15 member union
executive committee contains 3 Hispanics. What would be the probability of 3 or fewer Hispanics if the
executive committee were chosen at random from all the workers?
b.) A university is concerned about the academic standing of its athletes. A study committee chooses an
SRS of 50 of the 316 athletes to interview in detail. Suppose that in fact 40% of the athletes have been
told by their coaches to neglect their studies on at least one occasion. What is the probability that at least
15 in the sample are among this group?
12.) Use the methods from chapter 8, to find the probability in 11a.)
13.) According to a market research firm, 52% of all residential telephone numbers in Los Angeles are
unlisted. A telephone sales firm uses random digit dialing equipment that dials residential numbers at
random, whether or not they are listed in the telephone directory. The firm calls 500 numbers in Los
Angeles.
a.) What are the mean and standard deviation of the proportion of unlisted numbers in the sample?
b.) What is the probability that at least half the numbers dialed are unlisted? (Remember to check that
you can use the normal approximation).
14.) High School Dropouts make up 14.1% of all Americans aged 18 to 24. A vocational school that
wants to attract dropouts mails an advertising flyer to 25,000 persons between the ages of 18 and 24.
a.) If the mailing list can be considered a random sample of the population, what is the mean number of
high school dropouts who will receive the flyer?
b.) What is the probability that at least 3500 dropouts will receive the flyer?
15.) One way of checking the effect of undercoverage, nonresponse and other sources of error in a
sample survey is to compare the sample with known facts about the population. About 12% of American
adults are black. The proportion p̂ of blacks in an SRS of 1500 adults should therefore be close to 12%.
It is unlikely to be exactly 12% because of sampling variability. If a national sample only contains 9.2%
blacks, should we suspect the sampling procedure is somehow under representing blacks?
16.) The Gallup poll once asked a random sample of 1540 adults, “Do you happen to jog?” Suppose that
in fact 15% of all adults jog.
a.) Find the mean and standard deviation of the proportion p̂ of the sample who jog (Assume the sample
is an SRS.)
b.) Explain why you can use the formula for the standard deviation of p̂ in this setting.
c.) Check that you can use the normal approximation for the distribution of p̂ .
d.) Find the probability that between 13% and 17% of the sample jog.
e.) Find this probability for SRSs of sizes 200, 800, and 3200. What general conclusions can you draw
from your calculations?
17.) A USA Today poll asked a random sample of 1012 U.S. adults what they do with the milk in the
bowl after they have eaten the cereal. Of the respondents, 67% said they drink it. Suppose that 70% of
U.S. adults actually drink the cereal milk.
a.) Find the mean and standard deviation of the proportion p̂ of the sample that say they drink the milk?
b.) Explain why you can use the formula for the standard deviation of p̂ in this setting.
c.) Check that you can use the normal approximation for the distribution of p̂ .
d.) Find the probability of obtaining a sample of 1012 adults in which 67% or fewer say they drink the
cereal milk.
e.) What does your answer in part d.) tell you about the poll?
f.) What sample size would be required to reduce the standard deviation of the sample proportion to onehalf the value you found in part a.)?
g.) Find the probability that in a sample of 1012 adults, between 69% and 71% say they drink the cereal
milk.
Section 9-3
18.) The Wechsler Adult Intelligence Scale (WAIS) is a common IQ test for adults. The distribution of
WAIS scores is approximately normal with a mean of 100 and a standard deviation of 15.
a.) What is the probability that a randomly chosen individual has a WAIS score of 105 or higher?
b.) What are the mean and standard deviation of the average WAIS score x for an SRS of 60 people?
c.) What is the probability that the average WAIS score of an SRS of 60 people is 105 or higher?
d.)Would your answers to a.), b.) or c.) be affected if the distribution of WAIS scores in the adult
population was distinctly nonnormal? Explain
19.) The weight of the eggs produced by a certain breed of hen is normally distributed with mean 65
grams and a standard deviation 5 grams. Think of a carton of eggs as an SRS of size 12 from the
population of all eggs. What is the probability that the weight of a carton falls between 750 and 825
grams?
20.) A company that owns and services a fleet of cars for its sales force has found that the service lifetime
of disc brake pads varies from car to car according to a Normal distribution with mean μ = 55,000 miles
and standard deviation σ = 4500 miles. The company installs a new brand of brake pads on 8 cars.
a.) If the new brand has the same lifetime distribution as the previous type, what is the distribution of the
sample mean lifetime for the 8 cars?
b.) The average life on the pads on these 8 cars turns out to be x  51,800 miles. What is the probability
that the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged? (The
company takes this probability as evidence that the average lifetime of the new brand of pads is less than
55,000 miles.)