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Normal Distribution -6 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 ( X ) and Standard Deviation (s). • X • 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. .5 X .5 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 Deviation X Deviation Deviation Remember: if asked %, move decimal 2 places right and tack on the % sign Use the same value from the chart whether + or - 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? A).3413 .3413 .6826 68% B)0 .3413 .3413 34% C ).5 .3413 .1587 16% 180 150 X 210 240 120 90 270