Question: The following are the tax refunds ( payments ) from a population of people who had H&R Block complete their tax returns:

325 (125) (62) (71)

390 320 480 1163

800 (92) 720 820

700 1400 1100 310

1200 1300 1272 760

a) Make a histogram (15 points) Show your data table and the histogram graph. Show all of your calculations for full credit.

b) Calculate the average and standard deviation; assume a normal distribution. (15 points) Show all of your calculations for full credit.

c) Assuming a normal distribution, if I sample another 4 tax returns, what is the probability that the average of those 4 is less than 450? (25 points) Show all of your calculations for full credit.

d) I get a bonus of $50 for every return I complete with a refund over $750. I prepare 500 tax returns. What is my expected bonus? (25 points) Show all of your calculations for full credit.