1. 6.2 Use Normal Distributions
Pg. 219

2. Vocabulary Normal Distribution Standard Normal Distribution
Modeled by a “bell-shaped” curve
The “bell-shaped” curve is symmetric about the mean
Horizontal Reflection
Standard Normal Distribution
The normal distribution with a mean of 0 (zero) and a standard deviation of 1 (one).
The formula below can be used to transform -values from a normal distribution with mean ( ) and standard deviation into z-values having a standard normal distribution

3. Total area under curve equals 1.
Why?

5. A normal distribution has mean x and standard deviation σ
A normal distribution has mean x and standard deviation σ. For a randomly selected x-value from the distribution, find P(x – 2σ ≤ x ≤ x).
P( – 2σ ≤ x ≤ ) x =
= 0.475

6. A normal distribution has mean and standard deviation σ
A normal distribution has mean and standard deviation σ. Find the indicated probability for a randomly selected x-value from the distribution. x 1.
P( ≤ ) x
0.5
ANSWER

7. 81.5%
ANSWER

8. 3.
P( < < σ ) x
0.475
ANSWER

9. z - Score
The z–value for a particular –value (“mu” value) is called the z–score for the -value and is the number of standard deviations the –value lies above or below the mean .
To find the probability that z is less than or equal to some given value, we must use the table (pg 248)

10. The Normal Distribution

11. Example #2 Interpret normally distributed data
The heights of 3000 women at a particular college are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. About how many of these women have heights between 62.5 inches and 67.5 inches?
First find where 62.5 and 67.5 are on the bell curve.

12. Example #3
Use the Bell curve in #2 (pg 220)

13. Interpret normally distribute data
Health
The blood cholesterol readings for a group of women are normally distributed with a mean of 172 mg/dl and a standard deviation of 14 mg/dl.
a. About what percent of the women have readings between 158 and 186?
Readings higher than 200 are considered undesirable. About what percent of the readings are undesirable? b.

14. a. About what percent of the women have readings between 158 and 186?

15. Readings higher than 200 are considered undesirable
Readings higher than 200 are considered undesirable. About what percent of the readings are undesirable? b.

16. Homework
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