Question

5. Which score indicates the highest relative position? a. A score of 3 on a test with mean 4 and standard deviation b. A score of 610 on a test with mean 780 and standard deviation 100 c. A score of 42 on a test with mean 55 and standard deviation 6

Answer 1

a)

Here, μ = 4, σ = 1 and x = 3. We need to compute P(X <= 3). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (3 - 4)/1 = -1

b)
Here, μ = 780, σ = 100 and x = 610. We need to compute P(X <= 610). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (610 - 780)/100 = -1.7

c)

Here, μ = 55, σ = 6 and x = 42. We need to compute P(X <= 42). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (42 - 55)/6 = -2.17

A score of 3 indicates the highest relative position