Assume the average cost of a shower install in the United States is $4,500. Use this value as the population mean and assume that the population standard deviation is =$200. Consider a sampling distribution with sample size of 50 shower installs. Do not use Minitab and show all of your calculations.

a. What is the standard error of the mean for the distribution of sample means of insurance costs?

b. What is the probability that the sample mean is within $100 (between $4,400 and $4,600) of the population mean?

c. Find the sample mean shower install cost in which 40% of the sample mean shower install costs are less than it.

d. Consider that you selected a random sample of 30 shower installs and find that the sample mean is $4,450. Assume the population standard deviation is the same as above.Calculate a 90% confidence interval for the true population mean cost of shower installs. Does the true population mean from above fall within this interval?