The following table shows the number of overtime hours worked in one week per employee.

Question

Overtime hours 0 1 2 3 4 5 6

Number of employees 6 12 29 57 42 30 16

a) Define the random variable 𝑋.

(b) Constructtheprobabilitydistribution.

(c) Find the probability that a randomly selected employee;

(i) Worked exactly 3 hours

(ii) Worked more than 4 hours

(iii) Worked at most 3 hours

(iv) Worked between 2 and 5 hours, inclusive.

Answer 1

x = number of hours worked per week.

total number of employees = 192

Number of hours Number of Employees Probability

0 6 6/192 0.0313

1 12 12/192 0.0625

2 29 29/192 0.1510

3 57 57/192 0.2969

4 42 42/192 0.2189

5 30 30/192 0.1563

6 16 16/192 0.0833

(i) Worked exactly 3 hours 0.2969

(ii) Worked more than 4 hours 0.1563 + 0.0833

(iii) Worked at most 3 hours 0.0313+0.0625+0.1510+0.2969

(iv) Worked between 2 and 5 hours, inclusive. 0.1510+0.2969+0.2189+0.1563