In a certain city, the average 20- to 29-year old man is 69.8 inches tall, with a standard deviation of 3.1 inches, while the average 20- to 29-year old woman is 64.1 inches tall, with a standard deviation of 3.9 inches. Who is relatively taller, a 75-inch man or a 70-inch woman? Find the corresponding z-scores. Who is relatively taller, a 75-inch man or a 70-inch woman? Select the correct choice below and fill in the answer boxes to complete your choice.

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

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

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 taller?

Whoever has the higher z-score.

75-inch man

In a certain city, the average 20- to 29-year old man is 69.8 inches tall, with a standard deviation of 3.1 inches.

This means that .

We want Z when X = 75.

70-inch woman

The average 20- to 29-year old woman is 64.1 inches tall, with a standard deviation of 3.9 inches.

This means that

We want Z when X = 70.

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