# 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
(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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