Question

Suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 9. The teacher wishes to give A's to the top 7% of the students and F's to the bottom 7%. The next 17% in either direction will be given B's and D's, with the other students receiving C's. Find the bottom cutoff for receiving an A grade. (You may need to use the standard normal distribution table. Round your answer to the nearest whole number.)

Answer 1

The  bottom cutoff for receiving an A grade is 88.

What is the bottom cutoff for receiving an A grade?

The bottom cutoff for receiving an A grade is found as follows:

The mean of the distribution = 75

The standard deviation = 9

The z-score for the 93% = 1.476

The score for an A grade, x = mean + z-score * standard deviation

Score for an A grade, x = 75 + 1.476 * 9

Score for an A grade, x = 88

In conclusion, the minimum score for an A grade is obtained from the mean, the z-score and the standard deviation.

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