Probability statistics | Mathematics homework help

7.9 Suppose that we will take a random sample of size n from a population having mean f-L and standard
deviation (J’. For each of the following situations, find the mean, variance, and standard deviation of
the sampling distribution of the sample mean x:
a f-L=1O, (J’=2, n=25 C f-L=3, (J’=.1, n=4
b u. = 500, (J’ = .5, n = 100 d u. = 100, (J’ = I, n = 1,600
7.10 For each situation in Exercise 7.9, find an interval that contains (approximately or exactly)
99.73 percent of all the possible sample means. In which cases must we assume that the population
is normally distributed? Why?
7.32 Again consider the survey of 350 Bank of America customers discussed in Exercise 7.31, and
assume that 48 of Bank of America customers would currently express customer delight. That
is, assume p = .48. Find:
a The probability that the sample proportion obtained from the sample of 350 Bank of America
customers would be within three percentage points of the population proportion. That is, find
P(.45 :::; p :::; .51).
b The probability that the sample proportion obtained from the sample of 350 Bank of America
customers would be within six percentage points of the population proportion. That is, find
P(.42 :::; p :::; .54).
7.33 Based on your results in Exercise 7.32, would it be reasonable to state that the survey’s “margin of
error” is ±3 percentage points? ±6 percentage points? Explain.