An optical inspection system is used to distinguish among different part types. The probability of a correct classification of any part is 0.94. Suppose that three parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified.

An optical inspection system is to distinguish among different part types. The probability of a correct classification of any part is 0.94. Suppose that three parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified. Determine:

(a) the mean

(b) variance of X .

Round your answers to three decimal places

Solution:

Part A:

First we have to find the mean.

We have,

n = 3

p = 0.94

µ = n*p

Put the values in the formula:

µ = 3*0.94

µ = 2.82

Part B:

To find the Variance of X:

Var(X) = np(1 - p)

= 2.82(1 - 0.94)

= 2.82(0.06)

= 0.1692

By rounding off:

= 0.169