1. Unit 6 Section 5.2

2. 5.2: Normal Distributions: Finding Probabilities  A normal distribution curve can be used as a probability distribution.  Remember, normal curves are continuous, therefore there are no gaps in the curve (every z-score is represented).  Z-score represents distance from the mean (in standard deviations)

3.  If we were asked to find the P(0 < z < 1.5) we would determine the area under the standard normal curve from 0 to 1.5 standard deviations.  The value for the area represents the probability.  Remember, the probability can be written as a decimal or a percent.  Probabilities range from 0 to 1. Section 5.2

4.  Example 1 : Find the following: a)P(0 < z < 2.32) b)P(z < 1.65) c)P(z > 1.91) Section 5.2

5.  Example 2 A survey indicates that for each trip to a supermarket, a shopper spends an average of 45 minutes with a standard deviation of 12 minutes in the store. The lengths of time spent in the store are normally distributed and are represented by the variable x. a) Find the probability that the shopper will be in the store between 24 and 54 minutes. If 200 shoppers enter the store, how many would shop between 24 and 54 minutes? a) Find the probability that the shopper will be in the store more than 39 minutes. If 200 shoppers enter the store, how many would shop more than 39 minutes? Section 5.2

6.  We can also locate a z-score giving the areas under the standard normal curve by working backwards using your z-score table.  To find the z-score, locate the area on the table. Find the corresponding values in the left column and across the top row. Combine the values to arrive at the z-score. Section 5.2

7.  Example 3: Find the z value when the area under the standard normal distribution between 0 and the z value is 0.2123. Section 5.2

9. Homework:  Pg 249-250 : 1-6, 7-19 ODD Section 5.2