Question

A package delivery company experiences high variability in daily customer demand, which in turn results in high variability in the daily workload at the central sorting facility. The company relies on its sorting facility employees working overtime to provide on-time delivery when the workload demand is very high. A sorting facility employee receives a salary of $12/hour for a 40 hour week, and the employee receives $18/hour for every hour worked overtime, that is, for every hour worked over 40 hours in a given week. The number of overtime hours that an employee works in any given week is a random variable, with a mean of 15 hours and a standard deviation of 4 hours.
Required:
What are the mean, the standard deviation, and the variance of an employee's total weekly salary?

Answer 1

Solution :

Let :

X = number of overtime hours

S = total weekly salary

S = $12 \times 40 + 18 \times X$

S = 480 + 18X

E(S) = $480 + 18 \times E(X)$

$E(S) = 480 + 18 \times 15$

        = 750

Mean of S = 750

Var (S) = $18^2 \times Var(X)$

Var(S) = $18^2 \times 4^2$

          = 5184

Variance of S = 5184

The standard deviation equals square root of 5184 = 72