# BinomialWatch

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#1
I am completely stumped at how to approach and answer this question.

Use binomial theory to calculate error. A square golden slab was measured 2% too large. This measurement was used to calculate the amount of slabs needed for a square patio. The patio is required, by the customer, to be exactly 6m^2 (6 metres squared) and the slabs are 0.36m^2 (0.36 metres squared).

What would the resulting error in the area be?
What are your conclusions with respect to laying the patio?

I think it is just binomial expansion but, I do not have the area. I am expected to work this out (I am guessing it is 6m^2). Do I just find the 2% of 0.36m^2 which is 0.002592 and take that away with the 2% from one

(1 - 0.02)(1 - 0.002592)
(1 - 0.022592)
= 0.977408
= 97.74 Percentage error?

Or do I just divide 6^2 by 0.36^2 and find the area that way. I AM completely lost.
0
2 years ago
#2
(Original post by Joel Brown)
I am completely stumped at how to approach and answer this question.

Use binomial theory to calculate error. A square golden slab was measured 2% too large. This measurement was used to calculate the amount of slabs needed for a square patio. The patio is required, by the customer, to be exactly 6m^2 (6 metres squared) and the slabs are 0.36m^2 (0.36 metres squared).

What would the resulting error in the area be?
What are your conclusions with respect to laying the patio?

I think it is just binomial expansion but, I do not have the area. I am expected to work this out (I am guessing it is 6m^2). Do I just find the 2% of 0.36m^2 which is 0.002592 and take that away with the 2% from one

(1 - 0.02)(1 - 0.002592)
(1 - 0.022592)
= 0.977408
= 97.74 Percentage error?

Or do I just divide 6^2 by 0.36^2 and find the area that way. I AM completely lost.
I presume it means that the measurement of the side length of the square was 2% too large. Thus the overall scale factor applied to the true answer is 1.02^2 = 1.0404, i.e. the error is 4.04%, and the actual area built using the measured dimensions will be not 6 m^2, but 6*1.0404 =
6.2424 m^2. The number of slabs calculated will be 6.2424 / 0.36 = 17.34, so 18 slabs will be used, whereas the correct value should be 6 / 0.36 = 16.6666..., so 17 slabs should be used.
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