Respuesta :
Using the normal distribution, it is found that the z-score of the height of a women 5.5 feet tall is 0.51.
What is the missing information?
The problem asks for the z-score of the height of a women 5.5 feet tall.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
Considering that each feet has 12 inches, the parameters are given as follows:
[tex]X = 5.5 \times 12 = 66, \mu = 64.1, \sigma = 3.7[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (66 - 64.1)/3.7
Z = 0.51.
The z-score of the height of a women 5.5 feet tall is 0.51.
More can be learned about the normal distribution at https://brainly.com/question/15181104
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