Using the Empirical Rule The sample mean of the number of it

Using the Empirical Rule: The sample mean of the number of items in the lost and found at P33 Middle School in a given week is 15 items. With a standard deviation of 5 items.

What percentage of the time is the number of items in lost and found between 15 & 20?

Solution

The sample mean of the number of items in the lost and found at P33 Middle School in a given week is 15 items. With a standard deviation of 5 items

let X denote the number of items in the lost and found at P33 Middle school.

so X~N(15,5²)

so the probability that the number of items in lost and found between 15 & 20 is

P[15<X<20]=P[(15-15)/5<(X-15)/5<(20-15)/5]=P[0<Z<1] where Z~N(0,1)

                 =P[Z<1]-P[Z<0]=0.841345-0.5=0.341345=34.1345%

so the percentage of the time the number of items in lost and found between 15 & 20 is 34.1345% [answer]