Question

A professor in a large statistics class has a grading policy such that only the top 12% of the

students with the highest scores will receive the grade 1.0. The mean score for this class is

74 with a standard deviation of 6. Assuming that all the grades for this class follow a normal

probability distribution, what is the minimum score that a student in this class has to get to

receive a grade of 1.0?

Answer 1

Normal distribution mean =74

Standard deviation =6

Probability = 12%

Firstly needs to determine Z value using probability and normal distribution table.

Z = 1.175

$Z=\frac{x-\mu}{\sigma}$

$1.175=\frac{x-74}{6}$

$x-74=1.175\times6$

$x= 7.05 +74=81.05$

The minimum score that a student in the class has to get to receive a grade of 1.0 is 81.05.