On an exam with μ = 52,you have a score of X = 56.Which of the following values for the standard deviation would give you the highest position in the class distribution?
A)σ = 2
B)σ = 4
C)σ = 8
D)σ = 10

Question

On an exam with μ = 52,you have a score of X = 56.Which of the following values for the standard deviation would give you the highest position in the class distribution?​
A)​σ = 2
B)​σ = 4
C)​σ = 8
D)​σ = 10

Quizplus · Accepted Answer

To calculate your position in the class distribution, we need to find your z-score:

z = (X - μ) / σ

Plug in the values given in the problem:

z = (56 - 52) / σ

Solving for σ:

σ = (56 - 52) / z

To maximize your position in the class distribution, you want the lowest possible z-score. This means you want the highest possible value for σ.

Looking at the answer choices, the highest value of σ is D) σ = 10, but plugging that into the formula gives a z-score of only 0.4:

z = (56 - 52) / 10 = 0.4

On the other hand, choice A) σ = 2 gives a much lower z-score of 2:

z = (56 - 52) / 2 = 2

Therefore, the best choice would be A) σ = 2.

On an Exam with μ = 52,you Have a Score