Question

A concerned parents group determined the number of commercials shown in each of 5 childrens programs over a period of time. Find the standard deviation for the distribution shown.

Number of commercials X 5        6 7         8        9
Probability P (X)                     0.2    0.25    0.38 0.10 0.07

A.1.123

B.1.273

C.1.541

D.1.341

Answer 1

Solution:

Given that,

X	P(X)	X*P(X)	X^2*P(X)
5	0.2	1	5
6	0.25	1.5	9
7	0.38	2.66	18.62
8	0.1	0.8	6.4
9	0.07	0.63	5.67
Sum	1	6.59	44.69

Mean :

= X * P(X)

= 6.59

Standard deviation:

= X² * P(X) - ()²

= 44.69 - ( 6.59 )²

= 1.2619

= 1.123

Option A is correct.