This problem introduces an alternate empirical rule for Normal distributions. Th

Question

This problem introduces an alternate empirical rule for Normal distributions. This version has nice percentages instead of nice intervals. Part of this empirical rule is like the rule introduced in the book.

A recent study looked at the number of babies in the New England states who were born addicted to cocaine. It was found that the distribution of babies born each day who were addicted to cocaine was Normally distributed. This distribution has a mean of 60 babies and a standard deviation of 9. Using the empirical rule (as presented above), what is the approximate percentage of days in which the number of cocaine-addicted babies numbers between 39 and 78?

About 50% of all values fall within 2/3 standard deviations of the mean About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviations of the mean About 98% of all values fall within 2 1/3 standard deviations of the mean

Explanation / Answer

here z score for 39 =(X-mean)/std deviation =(39-60)/9=- 2 1/3

and z score for 78 =(X-mean)/std deviation =(78-60)/9=2

therefore percentage of days in which the number of cocaine-addicted babies numbers between 39 and 78

=P(-2 1/3 <Z<2) =(0.5+0.95/2)-(0.5-0.98/2) =0.49+0.475=0.965 ~ 96.5%

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