Significance with Range Rule of Thumb. In Exercises 29 and 30, assume that different groups of couples use the XSORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.

Gender Selection Assume that the groups consist of 36 couples.

a.Find the mean and standard deviation for the numbers of girls in groups of 36 births.

b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.

c. Is the result of 26 girls a result that is significantly high? What does it suggest about the effectiveness of the XSORT method?

It is given that 36 couples have tried the XSORT method to produce a baby. The probability of a girl is equal to 0.5.

a.

Here, the probability of a girl is given to be p=0.5.

The probability of a boy is computed below:

$$\begin{gathered} q=1-p \\ =1-0.5 \\ =0.5 \end{gathered}$$

The number of trials (n) is equal to 36.

Thus, the mean value is given as follows:

$$\begin{gathered} \mu =np \\ =\left(36\right)\left(0.5\right) \\ =18.0 \end{gathered}$$

Therefore, the mean number of girls is equal to 18.0.

The standard deviation is computed below:

$$\begin{gathered} \sigma =\sqrt{npq} \\ =\sqrt{\left(36\right)\left(0.5\right)\left(0.5\right)} \\ =3.0 \end{gathered}$$

Therefore, the standard deviation of the number of girls in 36 births is equal to 3.0.

b.

By using the range rule of thumb, the significantly low number of girls is computed below:

$$\begin{gathered} \mu -2\sigma =18.0-\left(2\right)\left(3.0\right) \\ =12.0 \end{gathered}$$

Thus, the significantly low number of girls is12.0 or less.

The significantly high number of girls are computed below:

$$\begin{gathered} \mu +2\sigma =18.0+\left(2\right)\left(3.0\right) \\ =24.0 \end{gathered}$$

Thus, the significantly high number of girls is24.0 or more.

Moreover, the values that are not significant will lie between 12.0 and 24.0.

Here, the value of 26 can be considered significantly high as it is greater than 24.0.

The value of 26 girls suggests that the XSORT method is effective.