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Probability, Statistics and Queueing

The dimension of a part follows a normal distribution with a mean of 50.0 mm and a standard deviation of 0.1 mm. Which of the following is closest to the fraction of parts whose dimension lies between 49.7 mm and 50.3 mm?

  1. AAbout 68%
  2. BAbout 95%
  3. CAbout 99.7%
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Answer: C. About 99.7%

49.7 to 50.3 mm is the mean ±0.3 mm, that is, ±3 standard deviations (±3σ). For a normal distribution, about 68% lies within the mean ±1σ, about 95% within ±2σ and about 99.7% within ±3σ (the 68-95-99.7 rule). The fraction in this range is therefore about 99.7%.

  • A. About 68% is the fraction within the mean ±1σ (49.9 to 50.1 mm).
  • B. About 95% is the fraction within the mean ±2σ (49.8 to 50.2 mm).
  • C. Correct. The range is ±3σ, so about 99.7%.
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