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 \\( \mu= \\) girl(s). (round to one decimal place as needed.) table of numbers of girls and probabilities

Explanation:

Step1: Recall the formula for the mean of a discrete probability distribution

The formula for the mean \(\mu=\sum_{x}x\cdot P(x)\).

Step2: Calculate each \(x\cdot P(x)\) term and sum them

• For \(x = 0\): \(0\times0.003=0\)
• For \(x = 1\): \(1\times0.031 = 0.031\)
• For \(x = 2\): \(2\times0.115=0.23\)
• For \(x = 3\): \(3\times0.221 = 0.663\)
• For \(x = 4\): \(4\times0.257=1.028\)
• For \(x = 5\): \(5\times0.219 = 1.095\)
• For \(x = 6\): \(6\times0.118=0.708\)
• For \(x = 7\): \(7\times0.034 = 0.238\)
• For \(x = 8\): \(8\times0.002=0.016\)

Now sum these values:

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Answer:

The mean is \(\mu = 4.0\) girl(s).