46. The average credit card balance for college seniors is $2864 (CNBC, October 19, 2006). Use this figure as the population mean and assume the population standard deviation is σ  $775.

Suppose that a random sample of 50 college seniors will be selected from the population.

a. What is the value of the standard error of the mean?

b. What is the probability the sample mean will be greater than $3000?

c. What is the probability the sample mean will be within $100 of the population mean?

d. How would the probability in part

(c) change if the sample size were increased to 100?