Discussion:
Q: A pet food manufacturer uses an automatic process to fill packages, which have a nominal weight of 40 pounds. Supposed that the actual weight is a normally distributed variable, with a mean of 40.9 pounds, and a standard deviation of 0.5 pounds.
a. What proportion of the individual bags contains less than 40 pounds?
b. If a sample of N=16 bags is selected, find the probability that the average for the sample exceeds 41 pounds.
c. If the sample of N=16 yielded a sample mean of 41.3 pounds, what would you conclude about the filling process, i.e., do you think that the population mean could still be 40.9 pounds? Explain.