Jorge scored 70 on an exam and his z-score was -2.00. Michelle scored 82 on the same test and her z-score was +1.00. What was the mean of the exam?
A) 74
B) 78
C) 84
D) Not enough information is provided.

Question

Quizplus · Accepted Answer

We know that the z-score formula is:

z = (x - mean) / standard deviation

We can rearrange this formula to solve for the mean:

mean = x - (z * standard deviation)

For Jorge, we know that his z-score is -2.00 and his score was 70. Therefore:

70 = mean - (2 * standard deviation)

For Michelle, we know that her z-score is +1.00 and her score was 82. Therefore:

82 = mean + (1 * standard deviation)

Now we have two equations with two unknowns (mean and standard deviation). We can solve for one of the unknowns and then substitute into the other equation to solve for the other unknown.

Let's solve for standard deviation first. We can rearrange the first equation as:

standard deviation = (mean - 70) / 2

Substituting this into the second equation, we get:

82 = mean + ((mean - 70) / 2)

Simplifying:

164 = 3 * mean - 70

3 * mean = 234

mean = 78

Therefore, the answer is B) 78.

Jorge Scored 70 on an Exam and His Z-Score Was