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Word problem with math/statistics

Posted on 2008-10-29
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Last Modified: 2012-05-05
Any help here?

Vending Machine: Soft drinks
u (mean) = 7.6 ; o(sd)= .4
(a) Estimate the probability that the machine will overflow an 8 oz cup
 = .1586 probability that the machine will overflow an 8 oz c.
(b) Estimate the probability that the machine will not overflow an 8 oz cup
 = .8585 probability that the machine will not overflow an 8 oz cup
(c) The machine just been loaded with 850 cups. How many of these do you expect will overflow when served?
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Question by:johntmcii
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Accepted Solution

by:
Infinity08 earned 480 total points
ID: 22832135
>> (a) Estimate the probability that the machine will overflow an 8 oz cup
>>  = .1586 probability that the machine will overflow an 8 oz c.

Correct. Using the cumulative distribution function for normal distributions :

        Phi(x) = [ 1 + erf((x - mu) / (sigma * sqrt(2))) ] / 2

with x = 8, mu = 7.6 and sigma = 0.4


>> (b) Estimate the probability that the machine will not overflow an 8 oz cup
>>  = .8585 probability that the machine will not overflow an 8 oz cup

This is the inverse of the result from (a), so 1 - 0.1586 = ...


>> (c) The machine just been loaded with 850 cups. How many of these do you expect will overflow when served?

Use the probability calculated in (a) for this ...
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Author Comment

by:johntmcii
ID: 22832335
so would you mind checking my work please?
(a) = .1586
(b) = .8414
(c) = .000186588 (lost on this one?)
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Assisted Solution

by:aburr
aburr earned 20 total points
ID: 22832341
There are a few minor difficulties with the numbers. u is the mean of what?
The probability of not overflowing and of overflowing do not add up to 1.
---
The probability of an overflow is 0.15. That is, if 100 cups were filled the most likely number of overflows would be 15. So one would expect, in your case, 850 x 0.1586 or 135 to overflow. What a mess. The janitor will insist that the machine be recallibrated.
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Author Comment

by:johntmcii
ID: 22832367
This is all regarding normal probability distributions (normal curves)
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LVL 53

Assisted Solution

by:Infinity08
Infinity08 earned 480 total points
ID: 22832436
>> (a) = .1586

>> (b) = .8414

Correct.



>> (c) = .000186588 (lost on this one?)

If you have 850 cups, and there is a probability of 0.1586 for each them to overflow, then how many of the 850 cups are expected to overflow ?
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Author Comment

by:johntmcii
ID: 22832462
850*.1586 = 134.81 or 135?
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Assisted Solution

by:Infinity08
Infinity08 earned 480 total points
ID: 22832507
>> 850*.1586 = 134.81

Correct. Rounding is not necessary (and if it is, then rounding up or down depends on what the value will be used for).
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Expert Comment

by:deighton
ID: 22832700
well 134.81 don't make sense for this case where there are 850 actual cups, so I'd give the answer as 135.

also, distribution is binomial, so

variance is (n.p.(p-1)) = 113.43

so s.d for number of cup overflows = 10.65, so for 3 standard deviations either side you've got between 102 and 167 failures being likely.
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LVL 18

Expert Comment

by:deighton
ID: 22832714
,although if people wanted not to round, it'd be fine with me.
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Author Comment

by:johntmcii
ID: 22832768
now i am confused again
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