Respuesta :
Answer:
The 75-inch man has the higher z-score, so he is relatively taller.
Step-by-step explanation:
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 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 [tex]\mu = 69.6, \sigma = 3[/tex]
We have to find Z when X = 75.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 69.6}{3}[/tex]
[tex]Z = 1.8[/tex]
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 [tex]\mu = 64.3, \sigma = 3.9[/tex]
We have to find Z when X = 70.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 64.3}{3.9}[/tex]
[tex]Z = 1.46[/tex]
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.
