1. According to the U.S. Census Bureau, the mean travel time to work for Pennsylvania workers is about μ = 26 minutes. Assume that standard deviation is σ = 6 minutes. Suppose that we take a sample of n = 30 Pennsylvania workers. Answer the following questions concerning , the sample mean.

a. Calculate the standard error of the sample mean.

b. Fill in the blanks for this specific scenario:

The sample mean follows a _____________________ distribution with mean ________ and standard deviation _________.

Hint: you should be using the value you calculated in part a in one of the blanks.

c. Follow the steps below to find the probability that in your sample of 30 workers, the mean travel time will be between 25 and 30 minutes, P(25< x^- < 30).

i. What are the z-scores for 25 and for 30? Your answer should include two values, one for each.

Hint: It may help to refer to part b.

ii. Using the values you calculated in part i, find P(25< x^- < 30) using the Standard Normal Table.

Hint: Recall that P(25< x^- < 30) = P( x^- < 30) - P(x^- < 25). So you'll have to look up two separate values in the Standard Normal Table and take the difference to solve this.

iii. Interpret, in the context of this problem, the value in part

ii. Keep in mind that the probability you've found concerns a sample mean.

d. Now suppose that we instead take a sample of size n = 60 from this population. Compared to our original sample size of n = 30, what happens to the distribution of the sample mean? It may help to think about the calculation of the standard error.