Question: A soft-drink bottle vendor claims that its production process yields bottles with a mean internal strength of 157 psi (pounds per square inch) and a standard deviation of 3 psi and is normally distributed. As part of its vendor surveillance, a bottler strikes an agreement with the vendor that permits the bottler to sample from the vendor’s production to verify the vendor’s claim.

a) Suppose the bottler randomly selects a single bottle to sample. What is the mean and standard deviation?

b) What is the probability that the psi of the single bottle is 1.3 psi or more below the process mean?

c) Suppose the bottler randomly selected 40 bottles from the last 10,000 produced. Describe the sampling distribution of the sample means?

d) What is the probability that the sample mean of the 40 bottles is 1.3 psi or more below the process mean?