Step 1 :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 23 couples.
Step 2 :We are asked to find the mean and the standard deviation for the numbers of girls in groups of 23 births.
Step 3 :The mean of a binomial distribution is given by the formula \(\mu = np\), where n is the number of trials (in this case, the number of couples, which is 23) and p is the probability of success (in this case, the probability of having a girl, which is 0.5). So, we need to calculate \(23 \times 0.5\) to find the mean.
Step 4 :The standard deviation of a binomial distribution is given by the formula \(\sigma = \sqrt{np(1-p)}\), where n is the number of trials, p is the probability of success, and sqrt is the square root function. So, we need to calculate \(\sqrt{23 \times 0.5 \times (1 - 0.5)}\) to find the standard deviation.
Step 5 :By calculating, we find that the mean is 11.5 and the standard deviation is approximately 2.4.
Step 6 :Final Answer: The mean number of girls in groups of 23 births is \(\boxed{11.5}\) and the standard deviation is \(\boxed{2.4}\) (rounded to one decimal place).