Question

Refer to the accompanying​ table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births

Number of Girls x	P(x)
0	0.006
1	0.026
2	0.107
3	0.214
4	0.277
5	0.225
6	0.115
7	0.027
8	0.003

The mean is μ = ___ girls? Round to one decimal place as needed.

Answer 1

Occurance(X)	Frequency(f)	Freq*X	(X-mean)	(X-mean)2	f*(X-mean)2
0	0.006	0	-4.018	16.144	0.097
1	0.026	0.026	-3.018	9.108	0.237
2	0.107	0.214	-2.018	4.072	0.436
3	0.214	0.642	-1.018	1.036	0.222
4	0.277	1.108	-0.018	0	0
5	0.225	1.125	0.982	0.964	0.217
6	0.115	0.69	1.982	3.928	0.452
7	0.027	0.189	2.982	8.892	0.24
8	0.003	0.024	3.982	15.856	0.048
Total ->	1	4.018	-	-	1.948

$mean =EX =\sum x*p(x) = 4.018$  ...(ANSWER)

$Var = (\sum X^2*P(x))-(EX)^2$

$= 1.948$

$SD=\sqrt{variance} = \sqrt{1.948} = 1.396$ ......(ANSWER