Question

Approximately 85% of persons age 70 to 84 live in their own household and are income-qualified for home purchases.

Answer 1

Answer:

The probability that exactly two of the four live in their own household and are income-qualified is  = .0975

Step-by-step explanation:

Given -

Approximately 85% of persons age 70 to 84 live in their own household and are income-qualified for home purchases.

Probability of sucess ( p ) = 85% =.85

Probability of failure ( q ) = 1 - .85 =.15

n = 4

From combination of n events taking r sucess we use binomial distribution

$P(X = r) = \binom{n}{r}p^{r}q^{n-r}$

where , r = 2

the probability that exactly two of the four live in their own household and are income-qualified is =

$P(X = 2) = \binom{4}{2}0.85^{2}0.15^{4 - 2}$

                = $\frac{4!}{(2!)(2!)} \times 0.7225 \times .0225$

                 = $6 \times 0.7225 \times .0225$

                 = .0975