5. The distribution of survival time of guinea pigs with cancer after treatment is typically strongly right-skewed. Assume that the mean of the guinea pig survival time for a population of guinea pigs with cancer is 100 days with a standard deviation of 10 days. Suppose we take a sample of size n=49 guinea pigs from the population of guinea pigs with cancer. (a) Explain why even though the population in this case is known to be skewed right we can model the sample mean using a Normal distribution. (b) What is the approximate probability that the sample mean survival time will be less than 95 days? (c) Determine the required sample size such that the probability that the sample mean will be within 2 days of the population mean survival time is 95%