Question

According to a survey of adults, 64 percent have money in a bank savings account. If we were to survey 50 randomly selected adults, find the mean number of adults who would have bank savings accounts.

Answer 1

The mean number of adults who would have bank savings accounts is 32.

Explanation:

For each adult surveyed, there are only two possible outcomes. Either they have bank savings accounts, or they do not. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

`E(X) = np`

In this problem, we have that:

`p = 0.64`

If we were to survey 50 randomly selected adults, find the mean number of adults who would have bank savings accounts.

This is E(X) when
`n = 50`.

So

`E(X) = np = 50*0.64 = 32`

The mean number of adults who would have bank savings accounts is 32.