Respuesta :
Answer:
a) [tex]Z = 2.69[/tex]
b) [tex]Z = 0.34[/tex]
c) The woman, because she has the higher z-score, that is, her height is more standard deviations above the mean.
Step-by-step explanation:
The z-score, which measures how many standard deviations a score X is above or below the mean, is given by the following formula.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
(a) What is the z-score for a woman who is 6 feet tall?
The heights of women aged 20 to 29 are approximately Normal with mean 65 inches and standard deviation 2.6 inches. This means that [tex]\mu = 65, \sigma = 2.6[/tex]
The mean and the standard deviation are in inches, so X is also must be in inches. Each feet has 12 inches. So X = 6*12 = 72 inches.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{72 - 65}{2.6}[/tex]
[tex]Z = 2.69[/tex]
(b) What is the z-score for a man who is 6 feet tall?
Men the same age have mean height 71 inches with standard deviation 2.9 inches. This means that [tex]\mu = 71, \sigma = 2.9[/tex]
The mean and the standard deviation are in inches, so X is also must be in inches. Each feet has 12 inches. So X = 6*12 = 72 inches.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{72 - 71}{2.9}[/tex]
[tex]Z = 0.34[/tex]
(c) Who is relatively taller?
The woman, because she has the higher z-score, that is, her height is more standard deviations above the mean.
