Question 6 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 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 We cannot tell b) What is the probability that the sample (n=36) 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 the population mean