Question

the random variable x represents the number of boys in a family of three children. assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable x.

a. mean: 1.50; standard deviation: 0.87
b. mean: 1.50; standard deviation: 0.76
c. mean: 2.25; standard deviation: 0.87
d. mean: 2.25; standard deviation: 0.76

Explanation:

Step1: Calculate the mean

The formula for the mean \(\mu\) of a discrete random variable is \(\mu=\sum_{x}x\cdot P(x)\).

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Step2: Calculate the variance

The formula for the variance \(\sigma^{2}=\sum_{x}(x - \mu)^{2}\cdot P(x)\)

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Step3: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{\sigma^{2}}\), so \(\sigma=\sqrt{0.75}\approx0.87\)

Answer:

A. mean: \(1.50\); standard deviation: \(0.87\)