2. A soft-drink bottle vendor claims that its process yields bottles with a mean internal strength of 157 psi (pounds per square inch) and a standard deviation of 3 psi. 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 50 bottles to sample. Based on the vendor's claim, what are the mean and the standard deviation of the average bottle strength of that sample? (10 points) b) Based on the vendor's claim, what is the probability, that the average bottle strength of the bottler's sample of 50 bottles is less than 156 psi? (10 points)