3. An astronomer takes 100 independent measurements X1,X2,,X100 of the unknown true distance in light-years between an observatory and a distant star. The measurement errors of these measurements are assumed to have a common distribution with mean 0 and standard deviation 2. The astronomer decides to use the sample mean of the measurements as the estimate for . (a) What is the probability that the estimate will be within 0.25 light-years of the actual distance ? (b) If the astronomer wants to be 95% sure that his estimate will be within 0.1 light-years of the actual distance , what is the required sample size?.