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.) table of numbers of girls and probabilities number of girls x p(x) 0 0.004 1 0.032 2 0.112 3 0.212 4 0.280 5 0.222 6 0.108 7 0.027 8 0.003

Explanation:

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

The formula for the mean \(\mu=\sum x\cdot P(x)\).

Step2: Calculate each \(x\cdot P(x)\) term

• When \(x = 0\), \(x\cdot P(x)=0\times0.004 = 0\)
• When \(x = 1\), \(x\cdot P(x)=1\times0.032=0.032\)
• When \(x = 2\), \(x\cdot P(x)=2\times0.112 = 0.224\)
• When \(x = 3\), \(x\cdot P(x)=3\times0.212=0.636\)
• When \(x = 4\), \(x\cdot P(x)=4\times0.280 = 1.12\)
• When \(x = 5\), \(x\cdot P(x)=5\times0.222=1.11\)
• When \(x = 6\), \(x\cdot P(x)=6\times0.108 = 0.648\)
• When \(x = 7\), \(x\cdot P(x)=7\times0.027=0.189\)
• When \(x = 8\), \(x\cdot P(x)=8\times0.003=0.024\)

Step3: Sum up all \(x\cdot P(x)\) terms

\(\mu=0 + 0.032+0.224 + 0.636+1.12+1.11+0.648+0.189+0.024\)
\(\mu=4.0\)

Answer:

\(4.0\)