Question

Problem

part A - In a large distribution of exam scores with a mean of 43 and a standard deviation of 12, what is the cutoff (minimum) score for person in the top 20% of the group?

Part b- In the same distribution, what are the boundary scores for those who score more than 25% of the group but up to 50% of the group? (The second Quartile).

Part C- - On a specific IQ test, with a mean of 100 and a standard deviation of 10, what is the Z-score associated with a score of 130?

Answer 1

Part A

We are given

µ = 43

σ = 12

For the top 20% area, we have

Z = 0.841621

(by using z-table or excel)

Cutoff score = µ + Z*σ

Cutoff score = 43 + 0.841621*12

Cutoff score =53.09945

Part B

For 25% area, Z = -0.67449

For 50% area, Z = 0

(by using z-table or excel)

Lower boundary = µ + Z*σ = 43 + (-0.67449)*12 = 34.90612

Upper boundary = µ + Z*σ = 43 + 0*12 = 43

Lower boundary = 34.91

Upper boundary = 43.00

Part C

We are given

µ = 100

σ = 10

X = 130

Z = (X - µ)/σ

Z = (130 – 100)/10

Z = 30/10

Z = 3