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 172 pounds and standard deviation is 12 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 We cannot tell
b)What is the probability that the sample (n=36) produce a sample mean of 175 pounds or higher, but will not exceed the weight limit ?
c)To calculate this probability, do you have to assume that the population is normal? Explain why or why not.