SOLUTION: 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 deviat

Algebra ->  Probability-and-statistics -> SOLUTION: 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 deviat      Log On


   

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.
Answer by Theo(13342) About Me  (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.