SOLUTION: Find the standard deviation of the random variable. 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,

Algebra ->  Probability-and-statistics -> SOLUTION: Find the standard deviation of the random variable. 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,       Log On


   

Question 868154: Find the standard deviation of the random variable.
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, respectively.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Note : Your probabilities do not sum to 1 but rather 0.9999.
Find the expected value mu
mu=0%280.6274%29%2B1%280.3102%29%2B2%280.0575%29%2B3%280.0047%29%2B4%280.0001%29
mu=0.4397
Now find the variance,
Var=sum%28x%5E2%2AP%28x%29-mu%5E2%29
Var=0%280.6274%29%2B1%280.3102%29%2B4%280.0575%29%2B9%280.0047%29%2B16%280.0001%29-0.1933%29
Var=0.5841-0.1933%29
Var=0.3908
sigma=sqrt%28Var%29
sigma=0.6251