A sign in the elevator in a factory indicates a limit of 36 persons. In addition, there is a weight limit of 6,400 pounds. Assume that the average weight of people working in this factory is 175 pounds and the standard deviation is 15 pounds. A random sample of 36 persons from the factory will be selected.
a) Completely describe the sampling distribution of the sample mean.
(i) Mean:
(ii) Standard deviation:
(iii) Shape: (just circle the correct answer)
Normal Approximately, normal Skewed, or We cannot tell
b) What is the probability that the sample (n=36) will produce a sample mean of 165 pounds or higher, but will not exceed the weight limit?
c) If your random sample (n=36) actually produced a sample mean equal to 190 pounds,
(i) Would you consider this unusual? Justify your answer with calculations.
(ii) What conclusion might you draw about the population mean?