ht on Statistics: Normal
The scores on a psychology exam were normally distributed with a me
the cutoff for a failing score? Approximately what percentage of the sti
The cutoff for a failing score was
(Simplify your answer.)

In a normal distribution, scores are spread out in such a way that about 68% of all scores fall within one standard deviation of the mean. If your cutoff for failing is, let’s say, one standard deviation below the mean, then this would put you in the bottom 16% of the distribution, as the bottom half of the scores account for 50% and then 16% beyond that. Therefore, about 16% of students would fail if that was the cutoff.

To find the exact cutoff, you can use the empirical rule (or 68-95-99.7 rule) which can help you visualize where that failing score would fall compared to the average scores. This method allows you to make quick calculations and understand how performance measures against the rest of the group. If you dig into z-scores and percentile ranks, you’ll find an even more robust way to determine exact cutoffs!