AP STATISTICS A particular moth can infest avocado trees and potentially damage the avocado fruit. A farmer plans to investigate the number of damaged avocado fruit on moth-infested avocado trees of a certain variety. A recent article states that the population distribution of the number of damaged avocado fruit on moth-infest avocado trees of this variety is symmetric but not mound-shaped with mean mu = 59 and standard deviation sigma = 24.

a) Compare the shapes of the sampling distributions of the sample mean number of damaged avocado fruit for random samples of 6 moth-infested trees and for random samples of 90 moth-infested trees from the population. Explain your answer.

b) Which of the following would be less likely to obtain from the population?
• A random sample of 36 moth-infested avocado trees having a mean number of damaged avocado fruit
that is less than 60 OR
• A random sample of 81 moth-infested avocado trees having a mean number of damaged avocado fruit
that is less than 60
Justify your answer.