In: Statistics and Probability
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
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