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It is given that the Rule of Three is utilized for finding the upper limit of the confidence interval when the number of successes is equal to 0.

Also, in a sample of 40 couples, each couple has a baby girl. The 95% upper bound for the population proportion (p) of boys is to be computed.

a.

One of the requirements for constructing a confidence interval estimate of the population proportion (using the formula given in the chapter) is that there should be at least 5 successes and at least 5 failures in that sample.

For a sample that has 0 successes and a confidence interval is to be constructed for the proportion of successes, the method discussed in the chapter cannot be used as the above-stated requirement is not fulfilled.

Therefore, the given formula cannot be applied.

b.

Let success be defined as having a baby boy.

Let p denote the population proportion of baby boys.

Here, the sample considered has no couple with a baby boy.

Thus, the number of successes is equal to 0.

Using the Rule of Three, which states that for a sample with n independent trials and number of successes equal to 0, the 95% upper bound of the population proportion has the following value:

$\frac{3}{n}$

For the given question, the value of n is equal to 40.

Using this rule, the 95% upper bound of p is computed below:

$$\begin{gathered} \frac{3}{n}=\frac{3}{40} \\ =0.075 \end{gathered}$$

Therefore, the 95% upper bound for the population proportion of boys is equal to 0.075.