Question

2. 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 9 and 15 days?

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

c) About what percent of the products last 6 days or less?

Answer 1

a) $P(9<X<15)=P(\frac{9-12}{3}<Z<\frac{15-12}{3})=P(-1<Z<1)=0.6826=68.26\%.$

b) $P(12<X<15)=P(\frac{12-12}{3}<Z<\frac{15-12}{3})=P(0<Z<1)=0.3413=34.13\%.$

c) $P(<6)=P(Z<\frac{6-12}{3})=P(Z<-2)=0.0228=2.28\%.$