In a certain city, the average 20- to 29-year old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20- to 29-year old woman is 64.3 inches tall, with a standard deviation of 3.9 inches. Who is relatively taller, a 75-inch man or a 70-inch woman?

The 75-inch man has the higher z-score, so he is relatively taller.

Step-by-step explanation:

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Who is relatively taller, a 75-inch man or a 70-inch woman?

We have to find the z-score for each of them. Whoever has the higher z-score is relatively taller.

75 inch man

In a certain city, the average 20- to 29-year old man is 69.6 inches tall, with a standard deviation of 3.0 inches.

This means that

We have to find Z when X = 75.

The man is 1.8 standard deviations above the verage 20- to 29-year old man.

70 inch woman

The average 20- to 29-year old woman is 64.3 inches tall, with a standard deviation of 3.9 inches.

This means that

We have to find Z when X = 70.

The woman is 1.46 standard deviations above the average 20- to 29-year old woman.

The 75-inch man has the higher z-score, so he is relatively taller.

part a: 1.08

part b: 27.59