Question

The results of a survey of 800 married couples and the number of children they had is shown below

Number of Children	Probability
0	0.1
1	0.3
2	0.4
3	0.2

(1) What is the standard deviation of the number of children in a family?

    a.  
0.92

    b.  
0.90

    c.  
0.81

    d.  
0.85

Answer 1

The below table helps us in finding the standard deviation

Number of Children (x)	Probability P(x)	x * P(x)	X2	X2 * P(x)
0	0.1	0	0	0
1	0.3	0.3	1	0.3
2	0.4	0.8	4	1.6
3	0.2	0.6	9	1.8
		x * P(x) = 1.7		x2 * P(x) = 3.7

Mean = x * P(x)

= 1.7

Standard Deviation = [ x² * P(x) ] - ²

= 3.7 - 1.7²

= 3.7 - 2.89

= 0.81

= 0.9

So Answer is Option B