A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. Below you will find probability and percentile calculations related to the customer purchase amounts.
a. What is the probability that a randomly selected customer will spend less than $15 at this store?
b. What is the probability that a randomly selected customer will spend $20 or more at this store?
c. What is the probability that a randomly selected customer will spend $30 or more at this store?
d. What is the probability that a randomly selected customer will spend between $20 and $35 at this store?
e. What two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values?
f. What two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values?