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Question 249:



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We need to compute the z-scores here, except we're given a sample mean so we need to modify the z-scores formula a bit. Instead of (x-mean)/sd we substitute the standard error of the sample mean (SEM) for the population standard deviation. The SEM is the standard deviation divide by the square root of the sample size. In this case it is 10/SQRT(25) = 10/5 = 2.

For a-c and convert the z-score to a percentile using the z-score to percentile calculator (select one-sided area).

a. (82-80)/2 = z of 1 The probability below a z of 1 is .8413

b. (76-80)/2 = z of -2. The probability below a z of 2 is0.227

c. (80-80)/2 = z of 0. The probability above a z of 0 is .50


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