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A professor has given the exact same exam for 30 years and finds that the mean...

A professor has given the exact same exam for 30 years and finds that the mean is 73 with a standard deviation of 8.4. Find the probability that a random sample of 40 students have an average grade greater than 81. Should the professor suspect cheating on the exam? The professor should suspect cheating if the probability is less that 5%, e.g. P(¯x > 81) < 0.05

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