The activity of a certain enzyme is measured by counting emissions from a radioactively labeled molecule. For a given tissue specimen, the counts in consecutive 10-second time periods may be regarded (approximately) as repeated independent observations from a normal distribution (as in Exercise 4.S.1). Suppose the mean 10-second count for a certain tissue specimen is 1,200 and the standard deviation is 35. For that specimen, let Y represent a 10-second count and let represent the mean of six 10-second counts. Both Y and are unbiased-they each have an average of 1,200-but that doesn't imply that they are equally good. Find Pr{ 1,175 < Y < 1,225} and Pr{ 1,175 <  < 1,225}, and compare the two. Does the comparison indicate that counting for 1 minute and dividing by 6 would tend to give a more precise result than merely counting for a single 10-second time period? How?