Question

A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 54.50 and a standard deviation of 9. If 67.66% of his students received grades of C or above, what is the minimum score of those students receiving a grade of at least a C

Answer 1

Students who receive a grade of at least a C must have a minimum score of 50.38.

Calculation of the minimum score

We may assume that the cut-off will be below 67.66 % because that percentage is more than 50%.

To get the value of 67.66 - 50 = 17.66, we must search in a regular normal table.

Hence, A z value of 0.458 will cause that value to occur.

Next, increase the standard deviation of 9 by 0.458.

The result is 4.122.

This indicates that the threshold for a student earning a C or higher is the mean minus 4.122.

So, the final result is 54.50-4.122 = 50.38.

Learn more about standard deviation here:

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