Question

The heights of adult women are approximately normal with a mean of 69.2 inches and a standard deviation of 2.5 inches. What is the height of the tallest 10

Answer 1

To find the height of the tallest 10% of adult women, calculate the z-score for a cumulative probability of 0.90 and use it to find the height.

Step-by-step explanation:

The question is asking for the height of the tallest 10% of adult women. To find this, we need to calculate the z-score corresponding to the top 10% of the standard normal distribution. Using the formula z = (x - μ) / σ where μ is the mean and σ is the standard deviation, we can find the z-score. Since we want to find the upper tail area, we use a z-table or calculator to find the z-score for a cumulative probability of 0.90. Once we have the z-score, we can calculate the height using the formula x = z * σ + μ.

Calculation:

Given: μ = 69.2 inches, σ = 2.5 inches, Cumulative probability = 0.90

1. Calculate the z-score for a cumulative probability of 0.90 using a z-table or calculator.
2. Plug the z-score into the formula x = z * σ + μ to find the height.