Question

4 6 0 The data given below show the number of overtime hours worked in one week per employee. Use the data to complete parts (a) and (b). Overtime hours 0 1 2 3 5 Employees 5 12 26 59 46 25 15 (a) Construct a probability distribution (b) Graph the probability distribution using a histogram and describe its shape. (a) Construct the probability distribution by completing the table below. 0 2 3 5 P(x) (Round to three decimal places as needed.) (6) Choose the correct graph of the probability distribution X 6 ОА, OB OC OD 0.4- 0.3 Probability 04 0.3 0.2 0.1 Probability 04- 0.3- 0.2- 0.11 Proty 0.2 0.1- 0.4 0.3 0.2 0.1 Probability 0 0 0- 0123456 Overtime Hours 0123456 Overtime Hours 0123456 Overtime Hours 0123456 Overtime Hours Describe the distribution's shape. Choose the correct answer below.

Answer 1

Solution=

The given data is,

Overtime Hours	0	1	2	3	4	5	6
Employees	5	12	26	59	46	25	15

a) Construct the probability distribution by completing the table below.

Here total number of employees is N = 188

Hence we can calculate the probabilities,

11 P(2) = N

i.e P0=4/188=0.027

similarly we calculate all probabilities.

P1=12/188=0.064 ,  ,

P2=26/188=0.138

P3=59/188=0.314

P4=46/188=0245

P5=25/188=0.133

P6=15/188=0.08

x	0	1	2	3	4	5	6
P(x)	0.027	0.064	0.138	0.314	0.245	0.133	0.08

b) Graph for probability distibution=

Option = C

Option A is the correct graph for the probability distibution.

The shape of the distibution is approximately symmetric (but not uniform).