Z-Score Problem Examples

Probability · Axiom Academy

EXAMPLE Z-Score Problem Examples Converting to standard normal, using Z-tables, and solving reverse problems Excellent work! You've completed this Z-score example. Here's what we learned: Forward Problem: Convert X to Z using Z = (X - μ)/σ, then use the Z-table to find probabilities. For X = 75, we got Z = 0.5 and P(X < 75) ≈ 0.691. Z-Table Usage: The standard normal table Φ(z) gives the cumulative probability P(Z ≤ z). Values are symmetric: Φ(-z) = 1 - Φ(z). Reverse Problem: Given a probability, find the corresponding z-value from the table, then convert back using x = μ + σz. 75th Percentile: Found z 0.75 ≈ 0.674 from the table, then calculated x = 70 + 10(0.674) = 76.74. Mastering Z-scores and tables is essential for working with any normal distribution problem!

This is the written version of the interactive lesson above. See the full Probability course.