1. Normal Distribution -6

2. Normal Distribution Probability distribution. It has the following important characteristics: (1) the curve has a single peak; (2) it is bell-shaped; (3) the mean (average) lies at the center of the distribution, and the distribution is symmetrical around the mean; (4) the two tails of the distribution extend indefinitely and never touch the horizontal axis; (5) the shape of the distribution is determined by its Mean ( ) and Standard Deviation (s).MeanStandard Deviation

3. As with any continuous probability function, the area under the curve must equal 1, and the area between two values of X (say, a and b) represents the probability that X lies between a and b as illustrated on Figure 1. Further, since the normal is a symmetric distribution, it has the nice property that a known percentage of all possible values of X lie within ± a certain number of standard deviations of the mean.

4. Adjust graph for information given Label the mean given. Adjust the standard deviation according to instructions Use the chart on the worksheet to calculate the probability. The bottom # of the curve that corresponds to the # on the chart. Mean of problem Deviation

5. Remember: if asked %, move decimal 2 places right and tack on the % sign Use the same value from the chart whether + or -

6. Example The shelf life of a particular snack chip is normally distributed with a mean of 180 days and a standard deviation of 30 days A) About what % of products last between 150 and 210 days? B) About what % of products last between 180 and 210 days? C) About what % of the products last more than 210 days? 150 120 210 240 180 90 270