Question

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

Answer 1

95th ​percentile = 68.86 inches.

Explanation:

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Answer 2

Answer: 68.86 inches

Explanation:

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

Mean :
`\mu=64.3\text{ inches}`

Standard deviation :
`\sigma=2.77\text{ inches}`

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 :-

`H=z*\sigma+\mu\\\\=1.6449*2.77+64.3=68.856373\approx68.86\text{ inches}`

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