The probabilities that a batch of 4 computers will contain 0,1,2,3,and 4 defective computers are 0.4746,0.3888,0.1195,0.0163,and 0.0008,respectively.Find the standard deviation of the number of defective computers.
A)0.75
B)0.56
C)1.01
D)0.70
E)0.87

Question

Quizplus · Accepted Answer

The standard deviation is the square root of the variance. The variance is the expected value of the squared deviation from the mean. The mean is the expected value. The expected value is the sum of the products of the values and their probabilities. The variance is the sum of the products of the squared deviations from the mean and their probabilities. The standard deviation is the square root of the variance.The mean is 0.4746*0 + 0.3888*1 + 0.1195*2 + 0.0163*3 + 0.0008*4 = 0.9492.The variance is 0.4746*(0 - 0.9492)^2 + 0.3888*(1 - 0.9492)^2 + 0.1195*(2 - 0.9492)^2 + 0.0163*(3 - 0.9492)^2 + 0.0008*(4 - 0.9492)^2 = 0.5625.The standard deviation is the square root of 0.5625, which is 0.75.

The Probabilities That a Batch of 4 Computers Will Contain