Question

Find the standard deviation of the random variable.

The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.5220, 0.3685, 0.0975, 0.0115, and 0.0005, respectively. Round the answer to two decimal places

Answer 1

Solution: Standard deviation calculate as follows

	P()	*P()	P()
0	0.522	0	0
1	0.3685	0.3685	0.3685
2	0.0975	0.195	0.39
3	0.0115	0.0345	0.1035
4	0.0005	0.002	0.008
Total	=1	=0.6	=0.87

Expected value or mean==E(X)= =0.60

Variance, = V(X)= E()-

=-

=0.87-0.36

=0.51

Variance, V(X)=0.51

Standard deviation====0.71

Standard deviation=0.71