The scores on a psychology exam were normally distributed with a mean of 58 and a standard deviation of 10. A failing grade on the exam was anything 2 or more
standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed?
To find the cutoff for a failing score, we need to calculate 2 standard deviations below the mean.
2 standard deviations below the mean = 2 * 10 = 20
Cutoff for failing score = mean - 2 standard deviations = 58 - 20 = 38
Therefore, the cutoff for a failing score is 38.
To find the percentage of students who failed, we need to calculate the area under the normal distribution curve below the cutoff for failing score.
Using a standard normal distribution table or calculator, we can find that the area to the left of 38 is approximately 0.0228.
Therefore, approximately 2.28% of the students failed the exam.