Webrooming, researching products online before buying them in store, has become the new norm for today's connected consumers; this is in contrast to show rooming, researching products in a physical store before purchasing online. A recent study by Interactions reported that most shoppers have a specific spending limit in place while shopping online. Findings indicate that men spend a mean of $250 online before they decide to visit a store.
(Data extracted from Retail Touchpoints, "88% of Shoppers Are Webrooming," bit.ly/1JEcmqh.) Assume that the spending limit is normally distributed and that the standard deviation is $20.
a. What is the probability that a male spent less than $210 online before deciding to visit a store?
b. What is the probability that a male spent between $270 and $300 online before deciding to visit a store?
c. Ninety percent of the amounts spent online by a male before deciding to visit a store are less than what value?
d. Eighty percent of the amounts spent online by a male before deciding to visit a store are between what two values symmetrically distributed around the mean?