All incoming freshman at a local university are given a diagnostic exam. The scores are normally distributed with a mean of 420, and a standard deviation of 45. If a student scores less than the "cut off score", they will have to retake the exam. Suppose 34% of the students did not pass, what is the "cut off score"? What we want is the data point, x, that will get us a percentage probability of 34%. We are given the mean and standard deviation. Since the percentage of students that did not pass is 34%, we can backtrack and first find the z that corresponds to a 34% probability. Z= Now we can find x by substituting in z, the mean, and standard deviation into the following relationship and solve for x. Z So, the cut off score for the exam is x =