Lab 5-Assignment You may complete the following questions by hand or using SAS/R. 1. Normal Distribution Computations: A certain manufacture produces batteries for television remotes. These batteries have a life expectancy that is normally distributed with a mean of 7 weeks and a standard deviation of 2 weeks.1 a) What is the probability that a randomly selected battery will last between 4 and 6 weeks? b) What is the probability that a randomly selected battery will last longer than 8 weeks? c) Joe collects a random sample of batteries of size 64 then records the sample average. Joe repeats this process 100 times recording the sample averages each time. Assuming independent sampling with replacement, what will (theoretically) be the mean of the sample averages be? What will (theoretically) the standard deviation of the sample averages be? d) In Joe's problem from part c, how would (if at all) the mean/standard deviation of the sampling averages change if the distribution of the battery life expectancy followed an Exponential distribution instead of a Normal distribution? 2. Central Limit Theorem Concept: Pretend I am a high school student who knows absolutely nothing about Statistics. Explain the