According to a 2018magazine, the average income in a state is $53,551. Suppose the standard deviation is $2,000 and the distribution of income isright-skewed. Repeated random samples of 1,600 aretaken, and the sample mean income is calculated for each sample. Complete parts(a) through(c).

a. The population distribution isright-skewed. Will the distribution of sample means beNormal? Why or whynot?

b. Find and interpret az-score that corresponds with a sample mean of $53,401.

c. Would it be unusual to find a sample mean of $53,890? Why or whynot?