Question

hours overtime 0,1,2,3,4,5,6
Employees 5,14,32,59,41,25,18
(a) construct a probability distribution
(b) Graph the probability distribution using a histogram and describe it's shape

Answer 1

a) Total employees = 5 + 14 + 32 + 59 + 41 + 25 + 18 = 194

Therefore the probability distribution here is obtained as:

Hours overtime(x)	Employees	P(X = x)
0	5	0.0257732
1	14	0.07216495
2	32	0.16494845
3	59	0.30412371
4	41	0.21134021
5	25	0.12886598
6	18	0.09278351
	194	1

Now this is constructed in EXCEL as a plot as:

b) The given distribution is plotted on a histogram as:

The given distribution is symemtric about the middle point and the peak lies at the center point. Therefore this is a symmetrical bell shaped kind of distribution.