The area of the bacteria-free zone on a Petri dish is known to be a random variable with a mean of 3.6 square cm and a standard deviation of 0.5 square cm. Suppose 100 such dishes are examined. (a) What is the approximate probability that the average will be less than or equal to 3.7 square cm? (b) Suppose you were now told that the area of bacteria-free zone is Normally distributed. Would this change your answer in part (a)? With this new information, would you need to apply the Central Limit Theorem in order to compute the probability in part (a)? Explain