Reference no: EM132848622

Over the past 50 supper evenings, a popular seafood restaurant has recorded the following data concerning daily customer orders of its very expensive 2-pound fresh lobster dinner platter.

X: Number of 2-pound fresh lobster dinner Frequency: # of evenings
platters ordered during the evening
12 22
14 12
16 8
18 6
20 2
Total 80 50
Figure 1. Lobster dinner data.

a. Let X be the number of 2-pound fresh lobster platters ordered by customers on any given evening. Construct a probability distribution for X, based on an analysis of the past 50 supper evenings, as described in the table above. Keep your calculations to two decimals.

b. Based on the probability distribution constructed in part a above, compute the mean number of 2-pound fresh lobster platters ordered per evening.

c. Based on the probability distribution constructed in part a above, compute the standard deviation of X.

d. The owners of the seafood restaurant are planning to follow the strategy of using the mean computed in part b above to guide them in terms of deciding how many 2-pound fresh lobster platters to serve, per supper evening, in the next month. Under what conditions -a large standard deviation or a small standard deviation-would they be more to likely experience severe problems relating to: either preparing insufficient lobster platters to satisfy daily customer demand, or preparing way too many lobster platters, resulting in a lot of food waste? Explain.