1. How do I use normal distributions in finding probabilities?
Thursday, November 4
Essential Questions
How do I use normal distributions in finding probabilities?

2. Use Normal Distributions
7.4
Use Normal Distributions
Standard Deviation of a Data Set
A normal distribution with mean x and standard deviation s has these properties:
The total area under the related normal curve is ____.
About ___% of the area lies within 1 standard deviation of the mean.
About ___% of the area lies within 2 standard deviation of the mean.
About _____% of the area lies within 3 standard deviation of the mean.
34%
34% x
– s
+ s
– 2s
+ 2s
– 3s
+ 3s
68%
95%
13.5%
13.5%
2.35%
2.35%
99.7% x
– 3s x
– 2s x
– s x
+ s x
+ 2s x
+ 3s
0.15%
0.15% x

3. Use Normal Distributions
7.4
Use Normal Distributions
Example 1
Find a normal probability x
– s
+ s
– 2s
+ 2s
– 3s
+ 3s
A normal distribution has a mean x and standard deviation s. For a randomly selected x-value from the distribution, find
Solution
The probability that a randomly selected x-value lies between _______ and _________ is the shaded area under the normal curve. Therefore:

4. Use Normal Distributions
7.4
Use Normal Distributions
Checkpoint. Complete the following exercise.
A normal distribution has mean x and standard deviation s. For a randomly selected x-value from the distribution, find x
– s
+ s
– 2s
+ 2s
– 3s
+ 3s

5. Use Normal Distributions
7.4
Use Normal Distributions
Example 2
Interpret normally distributed data
The math scores of an exam for the state of Georgia are normally distributed with a mean of 496 and a standard deviation of 109. About what percent of the test-takers received scores between 387 and 605?
169
278
387
496
605
714
823
Solution
The scores of 387 and 605 represent ____ standard deviation on either side of the mean. So the percent of test-takers with scores between 387 and 605 is

6. Use Normal Distributions
7.4
Use Normal Distributions
Checkpoint. Complete the following exercise.
In Example 2, what percent of the test-takers received scores between 496 and 714?
34%
13.5%
169
278
387
496
605
714
823

7. Use Normal Distributions
7.4
Use Normal Distributions
Example 3
Use a z-score and the standard normal table
In Example 2, find the probability that a randomly selected test-taker received a math score of at most 630?
Solution
Sep 1 Find the z-score corresponding to an x-value of 630.

8. Use Normal Distributions
7.4
Use Normal Distributions
Example 3
Use a z-score and the standard normal table
In Example 2, find the probability that a randomly selected test-taker received a math score of at most 630?
Solution
Sep 2 Use the standard normal table to find
The table shows that P(z < ____) = _______. z .0 .1 .2 -3
.0013
.0010
.0007 -2
.0228
.0179
.0139 -1
.1587
.1357
.1151 -0
.5000
.4602
.4207
.5398
.5793 1
.8413
.8643
.8849
So, the probability that a randomly selected test-taker received a math score of at most 630 is about ________.

9. Use Normal Distributions
7.4
Use Normal Distributions
Checkpoint. Complete the following exercise.
In Example 3, find the probability that a randomly selected test-taker received a math score of at most 620?

10. Use Normal Distributions
7.4
Use Normal Distributions
Pg. 277, 7.4 #1-21