Test runs with five models of an experimental engine showed that they operated, respectively, for 20, 18,22,17 and 18 minutes with 1 gallon of certain kind of fuel, A proposed specification states that the engine must operate for a mean of at least 22 minutes.
a) What can we conclude about the ability of the engine to meet the specification?
b) What is the probability that the sample mean could have come from a process whose true mean is equal to the specification mean?
c) How low would the mean operating minutes (of the engine population) have to be to have a 50% chance of concluding that the engine does not meet the specification?