It is estimated that 80% of all customers at Speedy Pizza prefer thin

crust pizza to thick crust pizza. The remaining 20% prefer thick crust pizza to thin

crust pizza. Of the many orders received by Speedy Pizza on a Friday night, six

separate orders fail to mention the type of crust desired. Unable to contact the six

customers and hoping to minimize disappointments, the manager of Speedy Pizza

has decided to send all of the six customers thin crust pizzas.

(a) Let X be the number of customers (among the six) who prefer the thin crust pizza.

What assumptions must be satisfied in order for X to obey a binomial distribution?

(b) Write down the probability distribution of X.

(c) What is the probability that exactly three of the six customers will prefer thick

crust pizza, and so be unsatisfied?

(d) What is the expected number of customers who will prefer thin crust pizza?

What is the standard deviation of the number of customers who will prefer thin

crust pizza?