The distribution of heights of adult American men is ...

[Pages:22] The distribution of heights of adult American men is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use the 68-95-99.7 rule to answer the following questions:

What percent of men are taller than 74 inches?

Between what heights do the middle 95% of men fall?

What percent of men are shorter than 66.5 inches?

A height of 71.5 inches corresponds to what percentile of adult male American heights?

2.2 More on Normal Distributions

and Standard Normal Calculations

Standardizing

The standardized value is called a z-score. x is the given value.

This tells you how many standard deviations you are from the mean.

This also allows you to find the percent of data under a given part of the curve.

z x

Who's Taller? (relatively speaking)

Verne is 67" tall. Assume the heights of women her age are normally distributed with a mean = 64 inches and standard deviation = 2.5 inches.

Hank is 72" tall. Assume the heights of men his age are normally distributed with a mean = 69.5 inches and standard deviation = 2.25 inches.

Example

The score for each student on a quiz is determined and a histogram is created from the data. It is bell-shaped and symmetric with a mean of 80 and standard deviation of 10. Interpret a zscore for a student who scored a 87 on the quiz.

Standardized Normal Curves

Recall our formula for standardizing normal curves.

z x

Since any normal curve can be standardized, we can find areas under the curve using one table, Table A. This table is found in the front of your book or in your folder.

Table A

It is very important to remember that Table A gives the area under the curve to the LEFT!!!

Also, standardized normal curves have a mean of 0 and a standard deviation of 1.

Reading Table A

Use Table A to find the proportion of observations that have a z-score less than 1.4 (this is 1.4 standard deviations from the mean).

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