1. Use Normal Distributions
Section 11.3

2. Objectives:
Find normal probabilities
Interpret normal distributions

3. Key Vocabulary: Normal distribution Normal curve
Standard Normal Distribution
z-score

4. Normal Distributions and Normal Curves
A normal distribution is modeled by a bell-shaped curve called a normal curve that is symmetric about the mean

5. Areas Under a Normal Curve (Page 757)

6. Example 1:
A normal distribution has mean and standard deviation σ. For a randomly selected x-value from the distribution, find

7. Example 2:
The blood cholesterol readings for a group of women are normally distribution with a mean of 172 mg/dl and a standard deviation of 14 mg/dl.
About what percent of the women have reading between 158 and 186?
Readings higher than 200 are considered undesirable. About what percent of the readings are undesirable?

8. #1: A normal distribution has mean and standard deviation
#1: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

9. #2: A normal distribution has mean and standard deviation
#2: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

10. #3: A normal distribution has mean and standard deviation
#3: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

11. #4: A normal distribution has mean and standard deviation
#4: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

12. #5: A normal distribution has mean and standard deviation
#5: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

13. #6: A normal distribution has mean and standard deviation
#6: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

14. Standard Normal Distribution
The standard normal distribution is the normal distribution with mean 0 and standard deviation 1. The formula below can be used to transform x-values into standard normal distribution. The z-value for a particular x-value is called the z-score and is the number of standard deviations the x-value lies above or below the mean.

15. Standard Normal Table
Page 759

16. Example 3:
Scientist conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each survey. The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of seals. Find the probability that at most 50 seals were observed during a survey.

17. #8: Complete.
In Example 3, find the probability that at most 90 seals were observed during a survey.

18. #9: Complete.
Explain why it makes sense that

19. Homework Assignment
Page 760 #4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 32, 34