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Question 702:



No answer provided yet.To answer these two questions we need to use the formula for a z-score for a data-points.  It is (x-μ)/s  where x is the datapoint, μ is the population mean and μ the population standard deviation.  While this is a sample, we cannot use the population data to compute the z-scores since that wasn't provided. Instead we need to infer based on the sample.

a. Using the formula we get (30-50)/10 = -2. We then lookup the value using a normal table or the
z-score to percentile calculator and the 1-sided area below is .0228 or 2.28% score below 30.
b. For between area questions we follow the procedure in a, except we repeat it for both values and subtract out the smaller area from the larger. So (30-50)/10 = -2 and  (55-50)/10 = .5 looking up the 2 1-sided areas we get .0228 and .691462. Subtracting the smaller gets us .691462-.0228 = .668712. Or there would be 66.87% of students scoring between 30 and 55.

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