Question

1. A soft drink bottler purchases glass bottles from a vendor. The bottles are required to have an internal pressure of at least 96.5 pounds per square inch (psi). A prospective bottle vendor claims that its production process yields bottles with a mean internal pressure of 97.1 psi and a standard deviation of 5 psi. The bottler strikes an agreement with the vendor that permits the bottler to sample from the production process to verify the claim. The bottler randomly selects 40 bottles from the last large batch produced, measures the internal pressure of each and finds the mean pressure for the sample to be 0.4 psi below the process mean cited by the vendor.

1. Assuming that the vendor is correct in his claim, what is the probability of obtaining a sample mean this far or farther below the process mean?
2. If the standard deviation were 1.3 psi as claimed, while if the mean were actually 96.9 psi, what is the probability of obtaining a sample mean of 96.6 psi or below?
3. If the process mean were 97.1 psi as claimed, while if the standard deviation were 1.8 psi, what is the probability of obtaining a sample mean of 96.7 psi or below?

Answer 1