# Statistics: Probabilities of normal distribution of ACT scores; poll for education vouchers

1. 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 60 students who took the exam is selected for study:

a) What is the shape, mean(expected value), and standard deviation of the sampling distribution of the sample mean score for samples of size 60?

b) What is the probability that the sample mean is 20 or higher?

c) What is the probability that the sample mean falls within 2 points of the population mean?

d) What value does the sample mean have be in order for it to be in the top 1% of the sampling distribution?

2. Last year, a national opinion poll found that 43% of all Americans 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 0.43. A random sample of 350 is to be selected and asked the same question.

a) What is the shape, mean(expected value), and standard deviation of the sampling distribution of the sample proportion for samples of size 350?

b) What is the probability that the sample proportion will fall within 0.03 of the population proportion?

3. Redo part (b) of problem 2, but assume that the sample size is 700. Does this answer make sense when compared to #2, part (b)? Why?

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#### Solution Preview

Please see the attached file for proper format.

PROBABILITY

1. 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 60 students who took the exam is selected for study:

a. What is the shape, mean(expected value), and standard deviation of the sampling distribution of the sample mean score for samples of size 60?

=µ =18.6

= = =0.7616

b. What is the probability that the sample mean is 20 or higher?

Here we can use Z ...

#### Solution Summary

This solution gives the step by step method for computing probabilities based on sampling distribution of sample proportion