Billy’s Bakery bakes fresh bagels each morning. The daily demand for bagels is a random variable with a distribution estimated from prior experience given by Number of Bagels Sold in One Day Probability 0 .05 5 .10 10 .10 15 .20 20 .25 25 .15 30 .10 35 .05 The bagels cost Billy’s 8 cents to make, and they are sold for 35 cents each.

Bagels unsold at the end of the day are purchased by a nearby charity soup kitchen for 3 cents each.

a. Based on the given discrete distribution, how many bagels should Billy’s bake at the start of each day? (Your answer should be a multiple of 5.)

b. If you were to approximate the discrete distribution with a normal distribution, would you expect the resulting solution to be close to the answer that you obtained in part (a)? Why or why not?

c. Determine the optimal number of bagels to bake each day using a normal approximation.

(Hint: You must compute the mean  and the variance 2 of the demand from the given discrete distribution.)