From an inventory of 18 cars being shipped to local dealers, 12 have had defecti

Question

From an inventory of 18 cars being shipped to local dealers, 12 have had defective radios installed. What is probability that one particular dealer receiving 8 cars obtains at most one with defective radios? Identify distribution. Find expectation and standard deviation Every day you test integrated circuits in sequence until you find the second failure and then stop. All test are independent with probability of failure p = .05. Let N be the number of tests. a)Identify distribution of R.V. N; find mean and variance. b) what is probability P(N>4)?

Explanation / Answer

Probability that a car has defective radio, p = 12/18 = 0.6667

If 8 cars are shipped, probability that at most 1 car will be defective
P(X<=1) = P(X=0) + P(X=1)

P(X=0) = (1-p)^8 = 0.00015
P(X=1) = 8C1 * p * (1-p)^7 = 0.0024

Hence required probability, P(X<=1) = 0.0026

This is binomial distribution.
Expected number of cars with defective radio = 0.6667 * 8 = 5.33
std. dev. = sqrt(npq) = sqrt(8*0.6667*0.3333) = 1.333

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