Question: You are a statistician for a life insurance company and notice that the monthly premium receipts appear to follow a normal distribution. After plotting receipts for a typical month and observing their distribution, you decide that the normality assumption is reasonable.

The insurance company wants to determine the percentage of monthly receipts that fall into the range $125 to $175, since such amounts are difficult to handle. They aren’t large enough to warrant investment attention, unless there are many of them, nor are they small enough to ignore by putting them into a cash account.

To find the percentage of accounts in this range you compute the mean and standard deviation of monthly premium receipts. You find the mean is $100 and the standard deviation is $39.

a. What percentage of monthly receipts can be expected to fall into the range of $125 to $175?

You predict that within two years the average monthly premium will rise to $150. If the standard deviation remains the same, how would this change the answer in (a)?