In a normal empirical distribution with Me = 100, SD = 15, and N = 200

Question

In a normal empirical distribution with Me = 100, SD = 15, and N = 200

A. Find the PR of Ezra who obtained a raw score of 120

B. If Joshua’s z-score was 0.8, what was his PR?

Answer 1

Given:

1. Mean (μ) = 100
2. Standard Deviation (σ) = 15
3. Raw Score (X) = 120
4. n = 200 (not needed to calculate percentile rank in a normal distribution)

Step 1: Calculate Ezra's Z-score

Z = (X−μ)/σ = (120−100)/15 = 1.33

Step 2: Find Percentile Rank (PR)

Look up Z = 1.33 in the standard normal distribution table.

P(Z<1.33) = ~0.9082

Ezra's PR = ~90.8

Given:

1. Joshua's z score = 0.8

Step 1: Find Joshua's PR

P(Z<0.8) = ~.7881

Hence Joshua's PR ~78.8