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**aptiva** **A sample of 200 people were given a test. The distribution of the test scores was mound-shaped and symmetrical with a mean of 100. One person, whose test score was 125, was found to be at the 84th percentile.**

a)Approximately how many people obtained scores between 65 and 85? __ANS: 38 people__

In the question it says that the mean is 100 and that one person got a score of 125 which was found to be at the 84th percentile.

So by the empirical rule (sorry not Chebyshev as i originally stated), 68% of the distribution is between -1s and +1s around the mean so half of that (34%) is betweent he mean and 1s above the mean so 50% + 34% = 84% which would mean that the std. dev. is 25

and so using the z-score, I find that 65-100/25 = 1.4 so a score of 65 corresponds to a standard deviation of 1.4 and a score of 85 corresponds to a standard deviation of 0.6 using the same formula

after this i kind of get stuck..