# Day Worker Probability

1. A group of day to day workers can work either 0 hours, eight hours or 12 hours at a pay rate of $9.75 per hour. (The 12 hour day pays regular time for the first eight hours and double time for the remaining four hours.) On any given day there is a 0.2 probability of not working at all, 0.7 probability of working an eight hour shift and a 0.1 probability of working a 12 hour shift.

a. What is the probability of working at least some of the time during a day?

b. What is the expected amount of work per day?

c. What is the variation in the expected amount of work per day?

d. What is the expected pay per day?

e. What are the expected earnings in a 5-day work week?

#### Solution Preview

... least some time) = 1 - P (not working at all)

= 1 - 0.2

= 0.8 (ANS)

b. What is the expected amount of work per day?

The expected value is the arithmetic mean, . To obtain it, we multiply each value of the random variable (the 0,8,12 hr) by its probability of occurrence and sum the products.

Let X be the amount of work per day,

E(X) = x P(X = x)

= 0*0.2 + 8*0.7 + 12*0.1

= 5.72 ...