4.28 A factory manager is considering whether to replace a temperamental machine. A review of past records indicates the following probability distribution for the number of breakdowns of this machine in a week.

Number of breakdowns 0 1 2 3 4 Probability 0.10 0.26 0.42 0.16 0.06

a. Find the mean and standard deviation of the number of weekly breakdowns.

b. It is estimated that each breakdown costs the company

$1,500 in lost output. Find the mean and standard deviation of the weekly cost to the company from breakdowns of this machine.