1. A local AT&T wireless retail center waits 4 days to receive a shipment of iPhones to replenish inventory (known as the lead-time). Demand during this lead-time period for iPhones follows the normal distribution with a mean of 50 phones and standard deviation of 9 phones.
a. Define the random variable and its probability distribution.
b. What is the probability that, during the next lead-time, demand for iPhones will be less than 42 phones?
c. What is the probability that, during the next lead-time, demand for iPhones will be less than 54 phones?
d. What is the probability that, during the next lead-time, demand for iPhones will be equal to 54 phones?