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Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The U.S. Army requires that the heights of women be between 58 and 80 inches. If 200 women want to enlist in the U.S. Army, how many would you expect to meet the height requirements? (Please round down to the nearest whole number.) 197 2 55 144 10 points Save Answer

Answer :

Answer:

Approximately 197 expect to meet the height requirement.

Step-by-step explanation:

Consider the provided information.

mean of 63.6 inches and a standard deviation of 2.5 inches.

Army requires that the heights of women be between 58 and 80 inches.

From the above information: μ=63.6 and σ=2.5

[tex]z=\frac{x-\mu}{\sigma}[/tex]

We need to find [tex]P(58<x<80)[/tex]

[tex]P(\frac{58-63.6}{2.5}<z<\frac{80-63.6}{2.5})[/tex]

[tex]P(-2.24<z<6.56)[/tex]

[tex]1-0.013=0.987[/tex]

Hence probability is 0.987.

If 200 women want to enlist in the U.S. Army then:

200×0.987≈197

Hence, approximately 197 expect to meet the height requirement.

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