To convert a z-score to a percentile, which operation is used?

• A. Percentile = Φ(z)
• B. Percentile = z
• C. Percentile = 1 - Φ(z)
• D. Percentile = e^z

Answer: (B)

Converting a z-score to a percentile uses the cumulative probability up to that z on the standard normal curve. That function, denoted Φ(z), gives P(Z ≤ z) for Z ~ N(0,1). In other words, it tells you the fraction of observations that fall at or below that z-value, which is exactly the percentile you’re after. So the percentile is Φ(z) (often expressed as a percentage by multiplying by 100).

The z-value itself is just a standardized score and doesn’t represent a probability. Expressions like z, 1 − Φ(z), or e^z don’t directly give the percentile.