Question

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.

Answer 1

To find the probability that at most two out of twelve DVD players are defective, we need to calculate the probabilities of having 0, 1, or 2 defective players and add them up. The probability of at most two defective players is 0.9080.

Step-by-step explanation:

To find the probability that at most two out of twelve DVD players are defective, we need to calculate the probabilities of having 0, 1, or 2 defective players and add them up.

The probability of 0 defective players is given by: P(X = 0) = (90/100)(89/99)(88/98)...(79/89)(78/88) = 0.2824

The probability of 1 defective player is given by: P(X = 1) = (10/100)(90/99)(89/98)...(80/90)(79/89) = 0.3833

The probability of 2 defective players is given by: P(X = 2) = (10/100)(9/99)(90/98)...(81/91)(80/90) = 0.2423

The probability of at most two defective players is the sum of these probabilities: P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2824 + 0.3833 + 0.2423 = 0.9080

Answer 2

µ = 2.82

Variance(X) = 0.169

Step-by-step explanation:

The complete question is:

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