Download CLT Example - Thomas P. Wakefield

Section 6.5: Additional Central Limit Theorem Problems
1. The national average SAT score is 1019. Suppose that nothing is known about the shape of the distribution and that the standard deviation is 100. If a random sample of 200 scores were selected at random
and the sample mean were calculated to be 1050, would you be surprised?
2. The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The
standard deviation is 8 minutes. Assume that the variable is normally distributed.
(a) Find the probability that a randomly selected adult will complete the test in less than 43 minutes.
(b) Find the probability that, if 50 randomly selected adults take the test, the mean time it takes the
group to complete the test will be less than 43 minutes.
(c) Does it seem reasonable that an adult would finish the test in less than 43 minutes? Explain.
(d) Does it seem reasonable that the mean of the 50 adults could be less than 43 minutes?
3. The standard deviation of a variable is 15. If a sample of 100 individuals is selected, compute the standard
error of the mean. What size sample is necessary to double the standard error of the mean? What size
sample is needed to cut the standard error of the mean in half?
Section 6.5: Additional Central Limit Theorem Problems
1. The national average SAT score is 1019. Suppose that nothing is known about the shape of the distribution and that the standard deviation is 100. If a random sample of 200 scores were selected at random
and the sample mean were calculated to be 1050, would you be surprised?
2. The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The
standard deviation is 8 minutes. Assume that the variable is normally distributed.
(a) Find the probability that a randomly selected adult will complete the test in less than 43 minutes.
(b) Find the probability that, if 50 randomly selected adults take the test, the mean time it takes the
group to complete the test will be less than 43 minutes.
(c) Does it seem reasonable that an adult would finish the test in less than 43 minutes? Explain.
(d) Does it seem reasonable that the mean of the 50 adults could be less than 43 minutes?
3. The standard deviation of a variable is 15. If a sample of 100 individuals is selected, compute the standard
error of the mean. What size sample is necessary to double the standard error of the mean? What size
sample is needed to cut the standard error of the mean in half?
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