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Café Kay currently does not sell chocolate cake. Suppose Café Kay is planning to sell chocolate...

Café Kay currently does not sell chocolate cake. Suppose Café Kay is planning to sell chocolate cake, and the number of sales for a randomly selected customer is a random variable with the probability function given below.

x

0

1

2

3

4

P(x)

0.19

?

0.28

0.16

0.07

a) Solve P(? = 1), as well as the mean number of sales and standard deviation (SD)

b) Solve the cumulative distribution function f(x), and plot f(x)

c) Suppose a customer buys a chocolate cake and pays £7. Each cake costs Café Kay £0.42. Define random variable Y = net profit for Café Kay (income - cake cost). Express Y in terms of X. Also solve the SD and mean net profit.

d) Based on your calculations above, if the distribution is true, should Café Kay sell chocolate cake? Why or why not?

Math   Statistics-And-Probability   
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