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 ( ) and Standard Deviation (s).

•

X

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 .5X

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.

X

Mean of problem

Deviation

Deviation

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?

X150

120

210

240

180

90270

).3413 .3413 .6826 68%

)0 .3413 .3413 34%

).5 .3413 .1587 16%

A

B

C