# statistics

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The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean of 18.6 and a standard deviation of 5.9. A simple random sample of 50 students who took the exam is selected for study:

A) What is the shape, mean, and standard deviation of the sampling distribution

of the sample mean for samples of size 50?

B) What is the probability that the sample mean is 21 or higher?

C) What is the probability that the sample mean falls within 2 points of the

population mean?

D) What is the probability that the sample mean is 17 or less?

Last year, a national opinion poll found that 44% of all American adults agree that parents should be given vouchers good for education at any public or private school of their choice. Assume that in fact the population proportion is 0.44. A sample of 300 is to be selected and asked the same question:

A) What is the shape, mean, and standard deviation of the sampling distribution

of the sample proportion for samples of size 300?

B) What is the probability that the sample proportion will fall within 3% of the

population proportion?

C) What is the probability that the sample proportion will exceed 50%?

D) If the sample size were increased to 900, what is the probability that the

sample proportion will fall within 3% of the population proportion

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