Answer to Question #324594 in Statistics and Probability for tatat

Question

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

Answer 1

$P\left( 12<X<15 \right) =P\left( \frac{12-12}{3}<\frac{X-12}{3}<\frac{15-12}{3} \right) =\\=P\left( 0<Z<1 \right) =\varPhi \left( 1 \right) -\varPhi \left( 0 \right) =0.8413-0.5=0.3413$

The percent is 34.13%