Question: You have a factory with 40 production machines that are essentially identical, each producing at a mean daily rate of 90 products with a standard deviation of 35. You may assume that they produce independently of one another. Consider the random variable "the average daily production per machine tomorrow."
a. Find the mean of this random variable. Compare it to the mean for a single machine.
b. Find the standard deviation of this random variable. Compare it to the standard deviation for a single machine.
c. What is the approximate probability distribution of this random variable? How do you know?
d. Find the approximate probability that your average daily production per machine will be between 95 and 100 products tomorrow.