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) Find the probability:

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

b) To determine the number of weeks, find the corresponding probability:

$$P(X<150)=P(Z< 42 150−250 ​ )=P(Z<−2.38)=0.0087.\\\space\\ N=52\cdot0.0087≈0.45<1.$$