Question

Mrs. Simpson’s calculus class has an exam with an average score of 80 and standard deviation of 15. Assume that exam scores are normally distributed. If Mrs. Simpson decides to give an A grade to students who score in the top 20% of the class, what exam score is needed in order to get the A grade? (3pts)

Answer 1

93 is the exam score needed in order to get the A grade in Mrs Simpson’s test

Explanation:

Let x be the score that gives an A grade

Mathematically from the z-score formula, we know that;

z-score = x-mean/SD

From the question, x = ? , mean = 80 and SD = 15

Thus;

z-score = x-80/15

But in this question, we have the probability but we do not have the z-score

So we need the z-score that is equivalent to 20%

20% is same as 0.2

Using the standard normal distribution table, a probability of 0.2 corresponds to a z-score of 0.84

Thus, mathematically;

0.84 = x-80/15

x-80 = 15(0.84)

x-80 = 12.6

x = 80 + 12.6

x = 92.6 which is approximately 93