Question

In a certain​ city, the average​ 20- to​ 29-year-old man is 69.4 inches​ tall, with a standard deviation of 3.2 inches, while the average​ 20- to​ 29-year-old woman is 64.5 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.

A. The​ z-score for the man,__, is larger than the​ z-score for the woman​,__, so he is relatively taller.
B. The​ z-score for the man,__, is smaller than the​ z-score for the woman​,__, so he is relatively taller.
C. The​ z-score for the woman,__, is larger than the​ z-score for the man​,__, so she is relatively taller.
D. The​ z-score for the woman,__, is smaller than the​ z-score for the man​,__, so he is relatively taller.

Answer 1

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


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.