Question

In a survey of women in a cortain country (ages 20-29), the mean height was 66.5 inches with a standard deriation of 2.94 inches. Answer the following questions about the specified normat distribution.

(a) What height ropresents the 95 th porcentlle?
(b) What height regresents the first euarile?
Cick to view oboe 1 of the inble, Cld to new sage 2 of the lable.
(a) The beight that rooresents the 0Seh peroentis is indes. (Fleund to two decimal places as neesed.)

Answer 1

The height that represents the 95th percentile is approximately 71.78 inches. The height that represents the first quartile is approximately 64.41 inches.

Step-by-step explanation:

a. The height that represents the 95th percentile can be found using the invNorm function. The formula to find the height is:

x = mean + (z * standard deviation)

where z corresponds to the z-score for the desired percentile. For the 95th percentile, z = 1.645. Substituting the given values, we have:

x = 66.5 + (1.645 * 2.94) = 71.78 inches

Therefore, the height that represents the 95th percentile is approximately 71.78 inches.

b. The height that represents the first quartile can be found using the same formula, but with a different z-score. The z-score for the first quartile is -0.674. Substituting the values, we have:

x = 66.5 + (-0.674 * 2.94) = 64.41 inches

Therefore, the height that represents the first quartile is approximately 64.41 inches.