Answer:
Height at the 20th percentile = 63.74
Step-by-step explanation:
We are given that the heights of women at a college are approximately Normally distributed with a mean of 65 inches and a population standard deviation of 1.5 inches.
Since, X ~ N(
)
The z score probability distribution is given by;
Z =
~ N(0,1)
As we are given that we have to find the height at the 20th percentile, which means the value of x below which the z has a area of 20% ;
P(X < x) = 0.20
P(
<
) = 0.20
P(Z <
) = 0.20
Now, in z normal table, the critical value of x having area less than 20% is -0.8416, i.e;
= -0.8416
x = 65 - (0.8416 * 1.5)
x = 65 - 1.2624 = 63.74 inches
Therefore, height at the 20th percentile is 63.74 inches .