es on a psychology exam were normally distributed with a mean of 66 and a standard deviation of 5. A failing grade on the exam was anything 2 or more
I 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.
Cutoff = Mean - (2 * Standard Deviation)
Cutoff = 66 - (2 * 5)
Cutoff = 66 - 10
Cutoff = 56
Therefore, the cutoff for a failing score is 56.
To find the percentage of students who failed, we need to calculate the area under the normal distribution curve below the cutoff score.
Using a standard normal distribution table or calculator, we can find the proportion of scores below 56. This proportion represents the percentage of students who failed.
However, since we do not have specific z-scores, we cannot provide the exact percentage of students who failed.