Question

refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. the random variable x represents the number of girls among 8 children. find the mean and standard deviation for the number of girls in 8 births. click the icon to view the data table. the mean is μ = girl(s). (round to one decimal place as needed.)

Explanation:

Step1: Identify the distribution type

This is a binomial distribution problem where \(n = 8\) (number of births) and the probability of having a girl \(p=0.5\) (assuming equal probability of having a boy or a girl).

Step2: Use the mean formula for binomial distribution

The mean of a binomial distribution is given by \(\mu=np\). Substituting \(n = 8\) and \(p = 0.5\), we get \(\mu=8\times0.5=4.0\).

Step3: Use the standard - deviation formula for binomial distribution

The standard deviation of a binomial distribution is \(\sigma=\sqrt{np(1 - p)}\). Substitute \(n = 8\) and \(p = 0.5\) into the formula: \(\sigma=\sqrt{8\times0.5\times(1 - 0.5)}=\sqrt{8\times0.5\times0.5}=\sqrt{2}\approx1.4\).

Answer:

The mean is \(\mu = 4.0\) girl(s). The standard deviation is \(\sigma\approx1.4\) girl(s).