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= 59 and standard deviation = 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
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
16) 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
and standard deviation = 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.
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