The scores on a psychology exam were normally distributed with a of 62 and a standard deviation of 8 . A failing grade on the exam wa anything 2 or more standard deviations below the mean. What was cutoff for a failing score? Approximately what percentage of the students failed? The cutoff for a failing score was 46 . (Simplify your answer.) Approximately \( \square \) percent of the students failed. (Round to one decimal place as needed.)

To find the cutoff for a failing score, you’ll subtract 2 standard deviations from the mean. Given a mean of 62 and a standard deviation of 8: Cutoff = Mean - (2 × Standard Deviation) = 62 - (2 × 8) = 62 - 16 = 46. Now, regarding the percentage of students who failed, you can refer to the properties of a normal distribution. About 95% of the scores should fall within two standard deviations of the mean, which means approximately 5% of students scored below 46, marking them as failing. So, the percentage of students who failed is approximately 5.0%.