  In a survey of women in a certain country (ages 20-29) the mean height was 66.8 inches with a standard deviation of 2.68 inches  Answer the following questions about the specified normal distribution.​(a) What height represents the 95th ​percentile? (b) What height represents the first​ quartile? (a) The height that represents the 95th percentile is _____  inches.    (Round to two decimal places as​ needed.)(b) The height that represents the first quartile is_____  inches.    (Round to two decimal places as​ needed.)

Question

In a survey of women in a certain country (ages 20-29) the mean height was

66.8 inches with a standard deviation of 2.68 inches
Answer the following questions about the specified normal distribution.
(a) What height represents the 95th percentile?
(b) What height represents the first quartile?

(a) The height that represents the 95th percentile is _____  inches.
(Round to two decimal places as needed.)
(b) The height that represents the first quartile is_____  inches.
(Round to two decimal places as needed.)
Step 1

The normal distribution:

A continuous random variable X is said to follow normal distribution with mean µ and standard deviation σ if the probability density function of X is,

Step 2

a.

Here the x value to the left of 95% represents the height at 95th percentile. Then the x value to the left of 95% or 0.95 proportion of the area under the distribution curve is calculated as follows:

Step 3

The value of x can be found by the Excel formula, “=NORM.INV(0.95, 66.8,2.68)”

By using the formula in Excel the x ...

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