2. In order to check on the manufacturing process, random samples of several tiles are taken repeatedly. According to the Central Limit Theorem, if a random sample of size n is drawn from a population with mean u and variance or, the sample mean has approximately a normal distribution with mean u and variance o'. The larger the sample size n, the better the approximation. Use the worksheet Normal Probabilities with 2=0.25 and use the worksheet to calculate the following probabilities: (a) What is the probability that the average number of flaws in a random sample of 10 tiles does not exceed 0.05? (b ) What is the probability that the average number of flaws in a random sample of 30 tiles does not exceed 0.05? Now suppose that the quality inspector is going to take a random sample of several tiles to estimate the average number of flaws. How likely is his estimate to be close to the true value? Which estimate is more likely to be beter, that one based on a sample of 10 tiles or the one based on a sample of 30 tiles? We will answer the above questions by simulation