A collection of values has a histogram that roughly follows the normal curve. A particular value is 2 SDs below the average. What is its percentile rank? Choose the answer that is closest.
Group of answer choices

10%

7%

12%

5%

2%


In a normal distribution, the standard deviation (SD) helps to determine how far a value is from the mean. When a value is 2 standard deviations (SDs) below the mean:

1. In a standard normal distribution, about **95%** of the values fall within 2 SDs of the mean (from -2 SD to +2 SD).
2. This means that the area to the left of -2 SD (below that point) represents 50% of the lower half of the distribution minus 47.5% (which is 95%/2). 
3. The remaining 2.5% is the area below -2 SD.

Therefore, the value that is 2 SDs below the mean corresponds to the **2.5th percentile**. Since the options provided are close estimates, the best matching choice is **2%**.

### Closest Answer: **2%**

Would you like to go over more details on how this works or ask another question?

Here are 5 related questions:
1. How do we calculate percentiles in a normal distribution?
2. What is the area between 1 and 2 standard deviations below the mean?
3. What is the difference between a z-score and a percentile rank?
4. How do we interpret percentiles in skewed distributions?
5. What does it mean for a value to be in the 50th percentile?

**Tip**: Percentile ranks are cumulative — a 20th percentile rank means 20% of values are below that rank.

A collection of values has a histogram that roughly follows the normal curve. A particular value is 2 SDs below the average. What is its percentile rank? Choose the answer that is closest. Group of answer choices: 10%, 7%, 12%, 5%, 2%.

Learn how to determine the percentile rank for a value that is 2 standard deviations below the mean in a normal distribution. This problem covers key statistical concepts, including the empirical rule and z-scores, suitable for students in Grades 10-12.

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