Answer :
Answer:
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]\mu = 69.8, \sigma = 3.1[/tex].
We want Z when X = 75.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 69.8}{3.1}[/tex]
[tex]Z = 1.68[/tex]
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 [tex]\mu = 64.1, \sigma = 3.9[/tex]
We want Z when X = 70.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 64.1}{3.9}[/tex]
[tex]Z = 1.51[/tex]
The 75-inch man has the higher z-score, so he is relatively taller.