ACT (Enhanced)MathematicsEasy
A quality control inspector is examining a batch of manufactured components. The weights of the components are normally distributed with a mean of 50 grams and a standard deviation of 2 grams. What percentage of components are expected to have a weight between 48 grams and 52 grams?
- A68%
- B95%
- C34%
- D99.7%
Show answer & explanationAnswer & explanation
Correct answer: A. 68%
The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. 48 grams is one standard deviation below the mean (50-2), and 52 grams is one standard deviation above the mean (50+2).
Why the other options are wrong
- B. This percentage corresponds to two standard deviations from the mean.
- C. This represents only one side of the mean (e.g., between mean and +1 SD).
- D. This percentage corresponds to three standard deviations from the mean.
Empirical Rule (68-95-99.7)
For a normal distribution, approximately 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.
- Applies specifically to normal (bell-shaped) distributions.
- Useful for quickly estimating data spread.
- Standard deviation is key to applying the rule.
Memory trick: 68-95-99.7: One, Two, Three deviations, you'll see!