In a survey of women in a certain country​ (ages 20minus​29), the mean height was 64.3 inches with a standard deviation of 2.77 inches. Answer the following question about the specified normal distribution. ​(a) What height represents the 95th ​percentile

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Answer: 68.86 inches

Step-by-step explanation:

Given : In a survey of women in a certain country having

Mean : [tex]\mu=64.3\text{ inches}[/tex]

Standard deviation : [tex]\sigma=2.77\text{ inches}[/tex]

The z-value corresponds to 0.095 is 1.645.  [Using standard normal distribution table]

The height that represents the 95th percentile is given by :-

[tex]H=z\times\sigma+\mu\\\\=1.6449\times2.77+64.3=68.856373\approx68.86\text{ inches}[/tex]

Hence, the height represents the 95th ​percentile = 68.86 inches.

Answer:

95th ​percentile = 68.86 inches.

Step-by-step explanation:

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