In a standard normal distribution, the z-score associated with the 97.5th percentile is which value?

In a standard normal distribution, the z-score associated with the 97.5th percentile is which value?

• A. 95th percentile
• B. 97.5th percentile
• C. 99th percentile
• D. 90th percentile

Answer: (B)

In a standard normal distribution, the z-score for a given percentile is the value z such that the probability P(Z ≤ z) equals that percentile. For the 97.5th percentile, the cumulative probability is 0.975, and the corresponding z-score is about 1.96. The question asks for the z-score associated with that percentile, but the options are listed as percentiles. The correct choice is the one that matches the same percentile level, i.e., 97.5th percentile. If you want the exact number, it’s approximately 1.96; other choices correspond to different percentiles (e.g., 95th ≈ 1.645, 99th ≈ 2.326, 90th ≈ 1.282).

In a standard normal distribution, the z-score for a given percentile is the value z such that the probability P(Z ≤ z) equals that percentile. For the 97.5th percentile, the cumulative probability is 0.975, and the corresponding z-score is about 1.96. The question asks for the z-score associated with that percentile, but the options are listed as percentiles. The correct choice is the one that matches the same percentile level, i.e., 97.5th percentile. If you want the exact number, it’s approximately 1.96; other choices correspond to different percentiles (e.g., 95th ≈ 1.645, 99th ≈ 2.326, 90th ≈ 1.282).