Question: Jake runs the concession stand for a Chicago area minor league baseball team. He knows that hot dog sales are normally distributed with an average of 600 hot dogs per day and a standard deviation of 50. Jake reconsiders how many hot dogs to buy after reading an article about Chicago area baseball. This article predicted good crowds for Chicago teams, which Jake believes will help his business.

a. Jake doesn't want to run out of hot dogs. If he can order each day how many hot dogs should he order so that the probability of running out is less than 2%.

Assume Jake orders the quantity you found in part (a). If you make a mistake in part (a) I will judge the rest of your work on the number you had in (a)

b. What is the probability that more than 50 hot dogs will be left over at the end of a day?

c. What is the probability that no more than 100 hot dogs will be left over at the end of a day?

d. Jake notices that over the past three weeks he has had five days where he ran out of hot dogs. What would you recommend to Jake and why? (Just saying order more is not sufficient. Do not try to come up a specific number to order.)

e. If Jake spends a $1.45 to sell a hot dog, and sells them for $2.00, what is the chance of Jake at least breaking even. Jake's fixed costs for his hot dog stand are $319.00. (Ignore the quantity you ordered in part a)