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Empirical Rule : If the histogram of the data is approximately mound shaped then
This is based on the normal distribution . Suppose X has a normal distribution with mean and standard deviation .
To determine the
form the z-scores
- About 68% of the data fall in the interval
- About 95% of the data fall in the interval
- About 99.5% of the data fall in the interval
Now call up the class code. The area under the curve to the left of Z1 = -1 is .1586. The area to the left of Z2 = 1 is .8413. Hence
or about 68%. The other two parts of the rule are obtained in the problems.