Families with 5 children are randomly selected find the expected number of boys a family might have

The expected number of boys a family might have is 2.5.

Step-by-step explanation:

Let X denote the number of boys in a family with 5 children.

The probability of a boy is, p = 0.50.

The child can either be a by or a girl independently.

The random variable X follows a binomial distribution with parameters n = 5 and p = 0.50.

The probability mass function is:

Compute the expected number of boys a family might have as follows:

x                                      p (x)                                           x · p (x)

0                

1                  

2                

3                

4              

5              

Then,

Thus, the expected number of boys a family might have is 2.5.

the answer is 62.8 cubic units