A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 8.75 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?
A) 85.00
B) 95.00
C) 87.92
D) 90.00

Question

Quizplus · Accepted Answer

To find the minimum score needed to receive an A grade, we need to find the score that is at the 8.75th percentile of the normal distribution of exam grades. Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the 8.75th percentile is approximately -1.18. 
We can then use the formula z = (x - μ) / σ, where x is the desired score, μ is the mean of 73, and σ is the standard deviation of 11, to solve for x. 
-1.18 = (x - 73) / 11 
-12.98 = x - 73 
x = 60.02 
Therefore, the minimum score needed to receive an A grade is 87.92 (since 60.02 is the minimum score at the 8.75th percentile of the distribution and an A corresponds to the top 8.75 percent of the grades).

A Professor at a Local University Noted That the Exam