Question

The following is the number of overtime hours worked by each employee at a company in a typical week.

(a)   [3pts Find the values to complete the probability distribution. Write these values in the table (round to 3 decimal places).

Overtime Hours	0	1	2	3
Employees	6	14	16	3
P(x)

(b)   [4pts] Compute the mean and standard deviation of the probability distribution, and write a sentence interpreting this.

Answer 1

Hours Employees   P(X)

0 6 0.154

1 14 0.359

2 16 0.410

3 3 0.077

b) Mean(E(X)) = 0 * 0.154 + 1 * 0.359 + 2 * 0.410 + 3 * 0.077 = 1.41

E(X^2) = 0^2 * 0.154 + 1^2 * 0.359 + 2^2 * 0.410 + 3^2 * 0.077 = 2.692

Variance = E(X^2) - (E(X))^2

= 2.692 - (1.41)^2

= 0.7039

Standard deviation = = 0.839

V0.7039