Question

The accompanying 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. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls.

The maximum value in this range is

(Round 1 decimal place)

The minimum value in this range is

(round 1 decimal place)

Based on the​ result, is 1 girl in 10 births a significantly low number of​ girls? Explain.

x   P(x)
0   0.004
1   0.012
2   0.043
3   0.115
4   0.196
5   0.234
6   0.197
7   0.114
8   0.038
9   0.016
10   0.031

Answer 1

E(X) = = 0 * 0.004 + 1 * 0.012 + 2 * 0.043 + 3 * 0.115 + 4 * 0.196 + 5 * 0.234 + 6 * 0.197 + 7 * 0.114 + 8 * 0.038 + 9 * 0.016 + 10 * 0.031 = 5.135

E(X^2) =  0^2 * 0.004 + 1^2 * 0.012 + 2^2 * 0.043 + 3^2 * 0.115 + 4^2 * 0.196 + 5^2 * 0.234 + 6^2 * 0.197 + 7^2 * 0.114 + 8^2 * 0.038 + 9^2 * 0.016 + 10^2 * 0.031 = 29.711

= E(X^2) - (E(X))^2

= 29.711 - (5.135)^2

= 3.343

= = 1.828

Maximum value = = 5.135 + 2 * 1.828 = 8.8

Minimum value = = 5.135 - 2 * 1.828 = 1.5

Yes, 1 girl in 10 births is a significantly low number of girls. Because 1 is less than the minimum usual value 1.5.