Question

In Test-1 of Math-120 you scored 85, where the mean score of the class is 70 and standard deviation = 5. On Math-150 Test-1 you scored 88, where the mean score on that class is 76 and standard deviation = 6. You did comparatively better on which test, Math-120 or Math-150? Show and explain your reasoning with the help of z-score.

Answer 1

For Math 120

Here, μ = 70, σ = 5 and x = 85. We need to compute P(X <= 85). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (85 - 70)/5 = 3

For math 150
Here, μ = 76, σ = 6 and x = 88. We need to compute P(X <= 88). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (88 - 76)/6 = 2

As z-score for Math-120 is greater than Math-150, the Math-120 performance is better than Math-150