Question

The accompanying data table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children.

x   P(x)
0   0.001
1   0.018
2   0.036
3   0.116
4   0.196
5   0.246
6   0.195
7   0.114
8   0.038
9   0.017
10   0.023

Find the maximum and minimum usual value.

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
0	0.001	0	0
1	0.018	0.018	0.018
2	0.036	0.072	0.144
3	0.116	0.348	1.044
4	0.196	0.784	3.136
5	0.246	1.23	6.15
6	0.195	1.17	7.02
7	0.114	0.798	5.586
8	0.038	0.304	2.432
9	0.017	0.153	1.377
10	0.023	0.23	2.3
Sum	1	5.107	29.207

Mean = = X * P(X) = 5.107

Standard deviation =

=X ² * P(X) - ²

=  (29.207 - 5.107²)

= 1.768

maximum usual value

= mean + 2 * Standard deviation

= 5.107 + 2 * 1.768

= 8.643

minimum usual value

= mean - 2 * Standard deviation

= 5.107 - 2 * 1.768

= 1.571