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

Question

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

Overtime hours	0	1	2	3	4	5	6
Number of employees	6	12	29	57	42	30	16

(a)  Define the random variable .

(b)  Construct the probability distribution.

(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.

(d)  Find the mean of the random variable .Explain your results

.

Answer 1

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

Overtime hours	0	1	2	3	4	5	6
Number of employees	6	12	29	57	42	30	16

The random variable is the number of overtime hours worked.

The probability for each of the overtime hours is the number of employees who work that hour/total number of employees, where the total number of employees is computed by summing the number of employees over all 7 categories. For example, for overtime hours 0, the probability would be 6/total number of employees. The sum of the probabilities will be equal to 1 (probably not exactly due to round-off error).

(i)             Worked exactly 3 hours = probability computed for hours = 3

(ii)           Worked more than 4 hours = sum of probabilities computed for hours = 5 and 6

(iii)          Worked at most 3 hours = sum of probabilities computed for hours = 0, 1, 2 and 3

(iv)          Worked between 2 and 5 hours, inclusive = sum of probabilities computed for hours 2, 3, 4 and 5.

The mean of the number of overtime hours worked is computed by summing overtime hours worked * probability over the 7 categories.