The mean of the scores obtained by a class of students on a physics test is 42. The standard deviation is 8%. Students have to score at least 50 to pass the test. Assuming that the data is normally distributed, % of the students passed the test.

Accepted Solution

We'll need to determine the z-score for the case where the mean is 42, the std. dev. is 8% and the passing score 50.  Then the area under the std. normal curve to the right of this z-score represents the # of students who pass.
        50 - 42             8
z = ---------------- = ----- = 1
              8                8

One way to answer this is to determine the area under the normal curve to the LEFT of z=1, and then subtract that area from 1.00.

Important fact:  68% of data values are found within 1 std. dev. of the mean; this means that 34% of data values are found between 0 and 1 std. dev.
Adding together the area under the normal curve to the left of z=0 (which is 0.50) and this 0.34 results in 0.84.  84% of students earned scores of less than 50.  (100%-84%) of the students earned scores of greater than 50.

Thus, 16% passed, 84% failed.