A planetary astrophysicist measures the density of the planet Neptune. After thousands of measurements he has determined that the average density is 1.64 g=cm3, and these measurements have a standard deviation of 0.5 g=cm3.
(a) If 25 measurements are selected at random from this data set, determine the probability that the average density is greater than 1.9 g=cm3.
(b) If 100 measurements are selected at random from this data set, determine the probability that the average density is greater than 1.7 g=cm3.