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Chapter 9 Quiz
AP Statistics
1.) Which of the following are true statements?
I. The larger the sample, the larger the spread in the sampling distribution.
II. Provided that the population size is significantly greater than the sample size, the
spread of a sampling distribution is about the same no matter what the population
size.
III. Bias has to do with the center, not the spread, of a sampling distribution.
(A) I and II
(D) I, II, and III
(B) I and III
(C) II and III
(E) None of the above.
2.) Which of the histograms represents the sampling distribution of p for p = 0.7 and n =
84?
(A)
(B)
(D)
(C)
(E)
3.) The distribution of weights of “16 ounce” potato chip bags is given
by the histogram on the right:
The distribution has a mean of 16.96 ounces with a standard deviation of 2.31 ounces. If
50 random samples of 12 bags each are picked, and the mean weight of each sample is
found, which of the following is most likely to represent the distribution of the sample
means?
(A)
(D)
(B)
(C)
(E) None of the above.
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.
4.) 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?
5.) Find the standard deviation for the number of dropouts. (Be careful.)
6.) Is the population of dropouts normally distributed? Can you assume the sampling
distribution is normally distributed? Explain.
7.) What is the probability that at least 3500 dropouts will receive the flyer? (Include a
sketch as part of your computation.)
8.) What is the probability that between 3000 and 6000 dropouts will receive the flyer?
The weight of chocolate bars is approximately normally distributed with a mean of 8
ounces and a standard deviation of 1.2 ounces.
9.) What is the probability that a randomly chosen chocolate bar weighs 10 ounces or
more?
10.) What are the mean and standard deviation of the average chocolate bar weight x for
an SRS of 32 bars?
11.) What is the probability that the average chocolate bar weight of an SRS of 32 bars is
10 ounces or higher?
12.) Would your answers to 9, 10, or 11 be affected if the distribution of chocolate bar
weights in the population were distinctly nonnormal. Explain.
13.) Suppose that you and your lab partner flip a coin 20 times and you calculate the
proportion of tails to be 0.7. Your partner seems surprised at these results and suspects
that the coin is not fair. Write a brief statement that describes why you either agree or
disagree with your partner. Be sure to provide support relating to the principles we have
discussed in Chapter 9.
14.) SAT Math scores are normally distributed with a mean of 500 and a standard
deviation of 100. If a random sample of 100 students had a mean SAT Math score of
525, would you describe these results as exceptional? Explain your answer.
15.) Children in kindergarten are sometimes given the Ravin Progressive Matrices Test
(RPMT) to assess their readiness for learning. Experiences at Southwark Elementary
School suggest that the RPMT scores for its kindergarten pupils have mean 13.6 and
standard deviation 3.1. The distribution is close to normal. Mr. Lavin has 22 children in
his kindergarten class this year. He suspects that their RPMT scores will be unusually
low because the test was interrupted by a fire drill. To check this suspicion, he wants to
find the level L such that there is probability only 0.05 that the mean score of 22 children
falls below L when the usual Southwark distribution remains true. What is the value of
L?
A MLB scout is checking out a minor league pitching prospect and, using a timer, finds
the average speed of his fastball to be 92.3 mph with a standard deviation of 2.3mph.
Assume the pitcher never tires and there is a consistent normal distribution of fastball
speeds.
16.) Would you check the timer if it registered 95 mph on the fastball? Explain.
17.) Would you check the timer if the next 30 fastballs averaged 95 mph?