Question

The ages of people who attend a local church are normally distributed. The mean age is 39.5, and the standard deviation is 18. Find the probability that a person chosen at random from this church is ages 21.5 or younger.

Answer 1

Answer:

15.9%.

Explanation:

The mean = 39.5

Standard deviation = 18

Raw Value, X=21.5

To find the probability that a person chosen at random from this church is ages 21.5 or younger, we first find the Z-Score.

$\begin{gathered} Z-\text{Score}=\frac{X-\mu}{\sigma} \\ =\frac{21.5-39.5}{18} \\ =\frac{-18}{18} \\ =-1 \end{gathered}$

Next, we check the P-Value from the Z-Table.

$P(x<21.5)=0.15866$

Therefore, the probability that a person chosen at random from this church is ages 21.5 or younger is 15.9%.