Airlines have recently toughened their standards for the weight of checked baggage, limiting the weight of a bag to 50 pounds on domestic U.S. flights. Heavier bags will be carried, but at an additional fee. Suppose that one major airline has stated in an internal memo to employees that the mean weight for bags checked last year on the airline was 34.3 pounds with a standard deviation of 5.7 pounds. Further, it stated that the distribution of weights was approximately normally distributed. This memo was leaked to a consumers’ group in Atlanta. This group had selected and weighed a random sample of 14 bags to be checked on a flight departing from Atlanta. The following data (pounds) were recorded:

What is the probability that a sample mean as small or smaller than the one for this sample would occur if the airline’s claims about the population of baggage weight is accurate? Comment on the results.