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 30 couples. complete parts (a) through (c) below.
a. find the mean and the standard deviation for the numbers of girls in groups of 30 births.
the value of the mean is \\( \mu = 15 \\).
(type an integer or a decimal. do not round.)
the value of the standard deviation is \\( \sigma = \square \\).
(round to one decimal place as needed.)

Explanation:

Step1: Identify the formula for standard deviation of a binomial distribution

The formula for the standard deviation of a binomial distribution is $\sigma=\sqrt{np(1 - p)}$, where $n$ is the number of trials and $p$ is the probability of success.

Step2: Substitute the values of $n$ and $p$ into the formula

Here, $n = 30$ (number of births) and $p=0.5$ (probability of a girl). So, $\sigma=\sqrt{30\times0.5\times(1 - 0.5)}$.

Step3: Simplify the expression inside the square - root

First, calculate $30\times0.5\times(1 - 0.5)=30\times0.5\times0.5 = 7.5$.

Step4: Calculate the square - root

$\sigma=\sqrt{7.5}\approx2.7$

Answer:

$2.7$