Suppose that a random sample of 40 power window mechanisms is taken from a lot of 5000 supplied to an auto manufacturer. Suppose that in the entire lot of 5000 mechanisms, the mean time to failure (under these high-stress conditions) is 5800 cycle and that the standard deviation is 2800. Each of the 40 sampled mechanisms is tested by putting it through continuous up-down cycle until it fails. The mean failure time for the sample is recorded.
What is the expected value of the sample mean?
What is the standard deviation of the sample mean?
What is the probability that the mean failure time for the sample is less than 3000 cycles?
What is the probability that a particular mechanism has a time to failure greater than 6500 cycles?