Question

The shelf life of particular dairy products is normally distributed with u of 12 days and o of 3 days .

a. About what percent of the products last between 9 and 15 days?

b. About what percent of the products last 6 days or less

c. If a delivery of dairy products weigh 320 kg. , how many kilograms is expected to last beyond 10 days

Answer 1

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

$=P(Z<1)-P(Z<-1)=0.6827=68.27\%.$

b. $P(X<6)=P(Z<\frac{6-12}{3})=P(Z<-3)=0.0013=0.13\%.$

c. $P(X>10)=P(Z>\frac{10-12}{3})=P(Z>-0.67)=1-P(Z<-0.67)=0.7486.$

$N=320*0.7486\approx 240.$