Question

9#Suppose that the heights of adult women in the United States are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. Yolanda is taller than 75% of the population of U.S. women. How tall (in inches) is Yolanda? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

Answer 1

66.7 inches

Explanation:

Given:

Mean (µ)= 65

Standard deviation (σ) = 2.5

We must calculate the value of z that represents 75% with the help of the normal table, just like this:

Therefore, z is approximately 0.675

Calculate Yolanda's height using the following formula:

`\begin{gathered} z=(x-µ)/(σ) \\ \\ \text{ We replacing:} \\ \\ 0.675=(x-65)/(2.5) \\ \\ x=0.675\cdot2.5+65 \\ \\ x=66.7\text{ in} \end{gathered}`

Yolanda's height is 66.7 inches