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Question 428:



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We can calculate a standard or z-score from the data by subtracting the data-point from the mean and dividing that result by the standard deviation. So a score of 62 has a z-score of (62-44)/7 = 2.57. We can now lookup the probability associated with a z-score of 2.57 by using the z-score to percentile calculator for 2-sided area. You should get about 1.02%. So it is unusual, but lets say 100 students made the observations. Given a mean of 44, we'd expect to see a score as extreme as 62 about 1 time out of 100. If we saw much more than 1 or 2, we'd suspect something was going on.

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