Question: Lucky Dogs sells spicy hot dogs from a pushcart. The owner of Lucky Dogs is open every day between 11:00 a.m. and 1:00 p.m. Assume the demand for spicy hot dogs follows a Poisson distribution with a mean of 50 per hour.
a. What is the probability the owner will run out of spicy dogs over the two-hour period if he stocks his cart with 115 spicy dogs every day?
b. How many spicy hot dogs should the owner stock if he wants to limit the probability of being out of stock to less than 2.5%?