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Your "friend", Tricky Joe, claims that apples from his orchard are larger than the applies from his competitor. Specifically, Tricky Joe tells you that his apples have a mean weight of 560g and standard deviation 40g. Being an intelligent consumer you want to verify Tricky Joe's claim before you agree to a purchase contract. You take a random sample of 100 apples from the orchard and obtain a mean sample weight of 540g.
a. What is the probability of obtaining a sample mean of 540g or less?
b. Does your sample give you reason to doubt Tricky Joe's claim? Explain.
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