Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $75 and standard deviation $20.

a. What is the probability that a randomly selected customer spends less than $85 at this store?

b. What is the probability that a randomly selected customer spends between $65 and $85 at this store?

c. What is the probability that a randomly selected customer spends more than $45 at this store?

d. Find the dollar amount such that 75% of all customers spend no more than this amount.

e. Find the dollar amount such that 80% of all customers spend at least this amount.

f. Find two dollar amounts, equidistant from the mean, such that 90% of all customer purchases are between these values.