Answer to Question #257323 in Statistics and Probability for gnat

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. a) About what percent of the products last between 10 and 12 days

Answer 1

The shelf life has the next distribution: $N(12,3^{2})=12+3N(0,1)$

a) About what percent of the products last between 10 and 12 days

The point is to find $P(10<12+3N(0,1)<12)$

$P(10<12+3N(0,1)<12) = P(-{\frac 2 3}<N(0,1)<0)=P(N(0,1)<0)-P(N(0,1)<-{\frac 2 3}) = 0.5 - 0.2525=0.2475$

About 24.75 percents of products will last between 10 and 12 days