Respuesta :
Using the normal distribution, we have that:
The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.
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.
The mean and the standard deviation of men's heights are given as follows:
[tex]\mu = 69.3, \sigma = 3.9[/tex].
The proportion of men who meet the height requirement is is the p-value of Z when X = 62 subtracted by the p-value of Z when X = 55, hence:
X = 62:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{62 - 69.3}{3.9}[/tex]
Z = -1.87
Z = -1.87 has a p-value of 0.0307.
X = 55:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 69.3}{3.9}[/tex]
Z = -3.67
Z = -3.67 has a p-value of 0.0001.
0.0307 - 0.0001 = 0.0306 = 3.06%.
The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.
More can be learned about the normal distribution at https://brainly.com/question/4079902
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