A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9.Only 5 percent of the students taking the test scored higher than what grade?
A)70.04
B)67.96
C)55.48
D)82.52

Question

Quizplus · Accepted Answer

To find the grade that only 5% of students scored higher than, we need to use the z-score formula:

z = (x - μ)/σ

Where: 
x = unknown grade 
μ = mean grade (69) 
σ = standard deviation (9)

We need to find the z-score that corresponds to the top 5% of the distribution. We can use a z-table or calculator to find the z-score that has an area of 0.05 in the right tail of the standard normal distribution.

Using a calculator, we get: 
invNorm(0.95) = 1.645

So, the z-score that corresponds to the top 5% of the distribution is 1.645.

Now we can solve for x:

1.645 = (x - 69)/9

x - 69 = 14.805

x = 83.805

Therefore, only 5% of students scored higher than 83.805, which is rounded to 82.52. So, the best choice is D.

A Set of Final Examination Grades in a Calculus Course