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. Complete the questions below. LOADING... Click the icon to view the data table. Use the range rule of thumb to identify a range of values containing the usual numbers of girls in 10 births. The maximum usual value is 0.2. ​(Round to one decimal place as​ needed.)x P(x)

0 0.004

1 0.017

2 0.043

3 0.112

4 0.206

5 0.234

6 0.202

7 0.114

8 0.041

9 0.011

10 0.016

Answer 1

From the given data, the following Table is calculated:

x	f	f x	f x2
0	0.004	0	0
1	0.017	0.017	0.017
2	0.043	0.086	0.172
3	0.112	0.336	1.008
4	0.206	0.824	3.296
5	0.234	1.17	5.85
6	0.202	1.212	7.272
7	0.114	0.798	5.586
8	0.041	0.328	2.624
9	0.011	0.099	0.891
10	0.016	0.16	1.6
Total =	1.00	5.03	28.316

Mean = = E(X) = 5.03

Variance = s² = E(X²) - (E(X))² = 28.316 - 5.03² = 3.0151

Standard Deviation =

Using Range Rule of Thumb:

Mean - 2 Standard Deviation = 5.03 - ( 2 X 1.7364) = 5.03 - 3.4728 = 1.5572

Mean + 2 Standard Deviation = 5.03 + ( 2 X 1.7364) = 5.03 + 3.4728 = 8.5028

So,

Answer is:

1.6 to 8.5