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Question 189:



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The so-called Normal Rule states that for a normal distribution (which we're assuming it is since the mean=median=mode):

  • 68% of the values fall within 1 standard deviation of the mean (plus or minus) 
  • 95% fall within 2 standard deviations (1.96 specifically) of the mean (plus or minus)

For part a) of the question we see that  285 and 315 are both 1 standard deviation above and below the mean (that's the plus or minus), so using the normal rule we say that 68% of the PVC pipes are between 285 and 315 mm.

For part b) we just need 2 standard deviations, which is 30, and add and subtract it from the mean to get 370 and 330. So roughly 95% of the PVC pipes will be within 370 and 330 mm. If you want slightly more precision, then we'd want 1.96 SD above and below the mean (1.96*15=29.4) to provide us with 329.4 and 270.6.

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