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Practice Chapter 7

1. Suppose the random variable X has a mean of 50 and a standard deviation of 10. Calculate the mean and the standard deviation of the sample mean for each of the following sample sizes:

a. n=35

b. n=50

c. n=75

d. n=100

e. What happens to the size of the standard deviation of the sample mean as the sample size increases?

2. The distribution of the number of people in line at a grocery store checkout has a mean of 3 and a variance of 9. A sample of the numbers of people in 50 grocery checkout lines is taken.

a. Calculate the probability that the sample mean is more than 4.

b. Calculate the probability that the sample mean is less than 2.5.

c. Calculate the probability that the sample mean differs from the population mean by less than 0.5.

3. A pollster claims that the mean amount spent on Christmas gifts by an American family is $927 with a standard deviation of $200. What is the probability that the mean amount spent on Christmas gifts for a sample of 500 families differs from the mean by less than $15.

4. The population proportion of voters who favor the candidate is .45. Find the mean and the standard deviation of the sample proportion for samples of the following sizes.

a. n=30

b. n=45

c. n=65

d. What happens to the size of the standard deviation of the sample proportion as the sample size increases?

5. Local nursery is waiting for its spring annuals to be delivered. And 20% of the plants ordered are petunias. If the first truck contains 120 plants packed at random, what is the probability that no more than 30 of the plants are petunias?