Question 625941: The probabilities that a batch of 4 computers will contain 0,1,2,3, and 4 defective computers are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectfully. Find the standard deviation for the probability distribution.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this is what i understand this to be:
x p(x) p(x)*x (x-mean)^2 (x-mean)^2*p(x)
0 0.6274 0 0.19333609 0.121299063
1 0.3102 0.3102 0.31393609 0.097382975
2 0.0575 0.115 2.43453609 0.139985825
3 0.0047 0.0141 6.55513609 0.03080914
4 0.0001 0.0004 12.67573609 0.001267574
mean >>>>> 0.4397
variance >>>> 0.390744576
standard deviation >>>> 0.625095654
mean is .4397
standard deviation is .625095654 which is the square root of the variance.
mean is calculated as x occurrences times the probability of x occurrences.
these are then all added up to get the mean.
variance is calculated as follows:
first you get x occurrences minus the mean.
then you square that.
then you multiply that by the probability of x occurrences
these are then all added up to get the variance.
than you take the square root of the variance to get the standard deviation.
Answer by ikleyn(52932)  (Show Source):
You can put this solution on YOUR website! .
The probabilities that a batch of 4 computers will contain 0,1,2,3, and 4 defective computers
are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectfully. Find the standard deviation for the probability distribution.
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I took the trouble / (the job) to add up all five of these given numbers and got 0.9999 as the sum.
There should have been a '1' here, then it would have been correct.
But the way it is presented in the post, it can only make you smile at how
illiterate or inaccurate are those who create and disseminate such problems.
So, my advise to the problem's creator is THIS:
- you either exclude this problem from the consideration,
or edit it in a way to make it perfect, as a Math problem should be.
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