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.

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x P(x)

0 0.005

1 0.018

2 0.044

3 0.117

4 0.198

5 0.245

6 0.206

7 0.114

8 0.037

9 0.015

10 0.001

Answer 1

Solution

Range rule of thumb states that the range is approximately four times the standard deviation.

$$SD(x) = \sqrt{ \sum {x^2P(x)} - {(\sum {xP(x)}}) ^2}$$

$$= \sqrt {27.225 - {4.949}^2} =1.652997$$

$Range = 4 SD(x)$

$=4(1.652997)=6.611988$

But

$$Range = max. \space value - min. \space value$$

$$Max. = \bar{x} + 2SD(x)$$ $$=4.949+2(1.652997) =8.254994$$

$$Min = \bar {x} - 2SD(x)$$ $$=4.949-2(1.652997) =1.643$$

Since

$Maximum \approx 9 \space$and $Minimum \approx 2$

1 girl in 10 births is a significantly low number of girls