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 95^{th} 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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