The annual commissions earned by sales representatives of Machine Products, Inc. a manufacturer of light machinery, follow the normal probability distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5,000.

a) What fraction of the sales reps earn more than $45,000 per year?

b) What fraction of the sales reps earn between $35,000 and $45,000?

c) What fraction of the sales reps earn between $33,000 and $35,000?

d) The sales manager wants to award the sales representatives who earn the largest commissions a bonus of $1,000. He can award a bonus to 25 percent of the representatives. What is the cutoff point between those who earn a bonus and those who do not?