Question

The following table represents a Discrete Probability Distribution for the number of days it takes John’s Garage to repair vehicles for its customers.

Number of days to repair a vehicle	1	2	3	4	5	6	7
Probability	26.7%	33.6%	15.8%	13.7%	6.3%	2.4%	1.5%

With the aid of a table, calculate the following

1. mean
2. variance, and
3. standard deviation

Answer 1

x	P(X=x)	xP(x)	x2P(x)
1	0.267	0.26700	0.26700
2	0.336	0.67200	1.34400
3	0.158	0.47400	1.42200
4	0.137	0.54800	2.19200
5	0.063	0.31500	1.57500
6	0.024	0.14400	0.86400
7	0.015	0.10500	0.73500
total		2.5250	8.3990
	E(x) =μ=	ΣxP(x) =	2.5250
	E(x2) =	Σx2P(x) =	8.3990
	Var(x)=σ2 =	E(x2)-(E(x))2=	2.0234
	std deviation=	σ= √σ2 =	1.4225

from above:

a) mean =2.525

b) variance =2.0234

c) standard deviation =1.4225