ACT (Enhanced)MathematicsEasy
A production manager is reviewing the efficiency of an assembly line. The number of defective units produced per hour follows a normal distribution with a mean of 15 units and a standard deviation of 3 units. What is the probability that in a given hour, the assembly line produces between 12 and 18 defective units?
- A34%
- B95%
- C68%
- D99.7%
Show answer & explanationAnswer & explanation
Correct answer: C. 68%
For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. The range of 12 to 18 units is exactly one standard deviation (3 units) below and above the mean (15 units).
Why the other options are wrong
- A. This represents the probability of being within one standard deviation on only one side of the mean.
- B. This represents the probability of being within two standard deviations of the mean.
- D. This represents the probability of being within three standard deviations of 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.
- Provides quick estimates of probability/data distribution.
- Standard deviation (σ) measures data spread from the mean (μ).
Memory trick: Normal curves love their 68-95-99.7 dance.