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The average weight of a set X of 100 bags of rice is 90 pounds , and the standard deviation is 8 pounds. Bag A weighs 2 standard deviations below the average weight and Bag B weighs 5 pounds more than Average.

Choose if quantity A or quantity B is bigger , equal or the information provided is not sufficient:

Quantity A: Difference between weight of Bag A and Bag B Quantity B: The range of weight of bags in set X

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  • $\begingroup$ using formula : mean+3*(sd) - mean - 3*(sd) where sd = standard deviation .. i used this formula but the answer said range cannot be calculated.. $\endgroup$ – Dinesh Pabbi Jan 3 '18 at 11:58
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Hint:

Without knowing how the data are distributed, how can we determine the range (to calculate quantity B) just from knowing the mean and standard deviation?

So, I feel the answer should be: Cannot be determined.

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    $\begingroup$ We cannot calculate quantity B exactly, but can we establish bounds on it? Clearly $B>0$, otherwise the standard deviation would be $0$. Also $B<90\cdot 100$ (99 bags of weight 0, one bag of weight $90\cdot 100$). Using all information in the question (weights are positive, mean=90, sd=8, one bag weighs 90-2 sd, another weighs 90+5), how tight could we make the bounds on B? Tight enough to decide if A is bigger? $\endgroup$ – Wouter Jan 3 '18 at 11:41
  • $\begingroup$ Hey your answer is right but cant we determine the range by using the standard deviation graph? And then using formula : mean+3*(sd) - mean - 3*(sd) where sd = standard deviation? i thought like this but your answer is right i still don't get why we can't calculate range? $\endgroup$ – Dinesh Pabbi Jan 3 '18 at 11:53
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    $\begingroup$ The formula you give, mean+3*(sd) - (mean - 3*(sd)) = 6*sd , is not a formula that gives you the range. Consider $\{0,2\}$: mean=1, sd=$\sqrt{2}$, range=2, 6sd$\neq$range. Or consider the beta distribution, which has range $[0,1]$ no matter the value of its standard deviation. $\endgroup$ – Wouter Jan 3 '18 at 12:22

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