Question

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 50 couples. Complete parts (a) through (C) below.

a. Find the mean and the standard deviation for the numbers of girls in groups of 50 births

Answer 1

The mean number of girls is 25, and the standard deviation is approximately 3.54 for groups of 50 births, assuming the probability of giving birth to a girl is 0.5.

Step-by-step explanation:

The question asks us to find the mean and standard deviation for the number of girls born in groups of 50 births, given that the probability of giving birth to a girl is 0.5 (assuming the gender selection method has no effect).

To find the mean (μ) of the number of girls, we use the formula for the mean of a binomial distribution, which is μ = n * p, where 'n' is the number of trials (births, in this case), and 'p' is the probability of a success (a girl being born). In this instance, μ = 50 * 0.5 = 25.

Next, we calculate the standard deviation (σ), using the formula for the standard deviation of a binomial distribution, which is σ = √(n * p * (1 - p)). Plugging in our values gives σ = √(50 * 0.5 * 0.5) = √(12.5) ≈ 3.54.

Therefore, the mean number of girls in groups of 50 births is 25, and the standard deviation is approximately 3.54.