Question

A peanut butter seller sells an average of 250 bottles of 1 kg week with a standard deviation of 42 kg. The sales are normally distributed.

a) If a sample of 16 weeks was selected for a study, find the probability that the sample mean is greater than 300 bottles

b) In one year how many weeks would record sales of less than 150 bottles

Answer 1

a) $P(\bar X>300)=P(Z>\frac{300-250}{\frac{42}{\sqrt{16}}})=P(Z>4.76)=1-P(Z<4.76)<0.0001.$

b) $P(X<150)=P(Z<\frac{150-250}{42})=P(Z<-2.38)=0.0087.$

Number of weeks: $N=52*0.0087\approx 0.45<1.$