Question

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(X 5.3.31 Question Help In a survey of women in a certain country (ages 20 - 29), the mean height was 64.9 inches with a standard deviation of 2.85 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 95th percentile? (b) What height represents the first quartile? Click to view page 1 of the table. Click to view page 2 of the table. (a) The height that represents the 95th percentile is (Round to two decimal places as needed.) inches. Enter your answer in the answer box and then click Check Answer. Clear All Check Answer

Answer 1

Given:  $\fn_phv \mu$ = 64.9 and standard deviation $\fn_phv \sigma$= 2.85

a)

We have asked to find the height(X) that represents the 95th percentile.

By using raw score formula.

X = Z_0.95 * $\fn_phv \sigma$ + $\fn_phv \mu$

= (1.645 * 2.85) + 64.9

= 69.59

Hence the height(X) that represents the 95th percentile is 69.59 inches.

b)

We have asked to find the height that represents the first quartile.

We know that first quartile divides lefts side 0.25 are from the right side 0.75

the height(X) that represents first quartile is-

X = Z_0.25 * $\fn_phv \sigma$ + $\fn_phv \mu$

= (-0.674 * 2.85) + 64.9

= 62.98

Hence the height(X) that represents the first quartile is 62.98 inches.

Hope this will help you. Thank you :)