the scores on a psychology exam were normally distributed with a mean of 61 and a standard deviation of 8. 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 students failed?
To find the cutoff for a failing score, we need to calculate 2 standard deviations below the mean.
Lower cutoff = Mean - (2 * Standard deviation)
Lower cutoff = 61 - (2 * 8)
Lower cutoff = 61 - 16
Lower cutoff = 45
The cutoff for a failing score is 45.
To find the percentage of students who failed, we need to calculate the area under the curve to the left of the cutoff.
Using a standard normal distribution table or calculator, we find that the area to the left of a z-score of -2 is approximately 0.0228.
Converting this to a percentage:
Percentage of students who failed = 0.0228 * 100
Percentage of students who failed = 2.28%
Approximately 2.28% of students failed.