Question

The beer store sells potato chips and has does so for a long time. Over the last four years, it has observed that its weekly demand for potato chips varies quite a bit from week to week, but does not follow any seasonal or predictable pattern. The volume of potato chips is much higher than beer, and the store estimates that weekly demand can be modeled as being normally distributed with a mean of 35 bags per week, and a standard deviation of 7.

Assume that the store has a given amount of inventory at the start of a week, and has no opportunity to replenish this inventory during the week. In particular for each of the question we’ll assume that the store has 34 bags of inventory at the start of the week.

Part A:

1. Based on the assumed normal distribution for demand, what is the probability that weekly demand is less than or equal to 30 bags? (rounded to three decimal places)

2. What is the probability that weekly demand exceeds 45 bags? (rounded to three decimal places)

Part B

1. What is the probability that it will sell all 34 bags? (rounded to three decimal places)

2. What is the probability that it has at least 2 bags of chips leftover at the end of the week? (rounded to three decimal places)

3. What is the probability that unmet demand equals or exceeds 3 bags? (rounded to three decimal places)

4. What is the expected number of bags that the store will sell? (rounded to three decimal places)

5. What is the expected number of bags in inventory at the end of the week? (rounded to three decimal places)

6. What is the expected unmet demand? (rounded to three decimal places)

Answer 1