| Question : A sample of PVC pipes coming off a production line were tested for pipe diameter size. The statistical results (in millimeters) were:
Mean 300
Median 300
Mode 300
Standard Deviation 15
Range 90
Number in Sample 100
a) According to the Normal Rule, what percent of the pipes had diameters between 285 and 315?
b) What would the range of pipe diameters need to be in order to capture 95% of the pipe diameters? Answer : The so-called Normal Rule states that for a normal distribution (which we're assuming it is since the mean=median=mode):
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. | How helpful was this answer?
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