Use the Poisson model to approximate the probability. Round your answer to four decimal places.
-The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 150 calls received by the switchboard, there are at least
Two wrong numbers.
A) 0.8009
B) 0.5768
C) 0.1991
D) 0.2240
E) 0.7760

Question

Quizplus · Accepted Answer

The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known average rate. The Poisson distribution is given by the formula:$$P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}$$where:* X is the number of events that occur* k is the specific number of events that you are interested in* λ is the average number of events that occurIn this case, we are interested in the probability of getting at least two wrong numbers out of 150 calls. The average number of wrong numbers is 150 * 0.02 = 3. So, the probability of getting at least two wrong numbers is:$$P(X \geq 2) = 1 - P(X = 0) - P(X = 1)$$$$= 1 - e^{-3} \frac{3^0}{0!} - e^{-3} \frac{3^1}{1!}$$$$= 1 - 0.0498 - 0.1494$$$$= 0.8009$$Therefore, the correct answer is A) 0.8009.

Use the Poisson Model to Approximate the Probability