The basal diameter of a sea anemone is an indicator of its age, and in a certain population of anemones, the distribution of basal diameters is approximately normal with a mean of 5.3 cm and a standard deviation of 1.8 cm. Suppose you randomly select five anemones from this population.
1. What is the probability that all five anemones have a basal diameter more than 5.5 cm?
2. What is the probability that the mean basal diameter of the five anemones is more than 5.5 cm?
3. Comparing the probabilities you calculated in parts (1) and (2), which is larger?
Even if we changed the values the mean and standard deviation of this population, briefly explain why this must will always be the case.