Question

Suppose the heights of women at a college are approximately Normally distributed with a mean of 66 inches and a population standard deviation of 1.5 inches. What height is at the 35thpercentile?

Answer 1

Given data:

Mean: 66 in

Standard deviation: 1.5in

Find height is at the 35th percentile

Use the formula to find the z-score:

`z=(x-\mu)/(\sigma)`

z is the z-score corresponding to an area of 0.35 in the normal curve (35th percenlite)

μ is 66in

σ is 1.5in

Find the value of x corresponding to the given percentile:

1. Use a z-table to find the z score:

z=-0.39

2. Use the formula of z score and the given data to solve x:

`\begin{gathered} -0.39=(x-66)/(1.5) \\ \\ 1.5(-0.39)=x-66 \\ \\ -0.585=x-66 \\ \\ -0.585+66=x \\ \\ x=65.415 \end{gathered}`Then, the 35th percentile is 64.4 inches