Determine the required probability by using the Poisson approximation to the binomial distribution. Round to threedecimal places.
-The probability that a call received by a certain switchboard will be a wrong number is 0.01. Use the Poisson approximation to the binomial distribution to find the probability that among 120 calls
Received by the switchboard, there are at least two wrong numbers.
A)0.337
B)0.217
C)0.121
D)0.663

Question

Determine the required probability by using the Poisson approximation to the binomial distribution. Round to threedecimal places.
-The probability that a call received by a certain switchboard will be a wrong number is 0.01. Use the Poisson approximation to the binomial distribution to find the probability that among 120 calls
Received by the switchboard, there are at least two wrong numbers. 
A)0.337
B)0.217
C)0.121
D)0.663

Quizplus · Accepted Answer

The Poisson approximation to the binomial distribution is appropriate when the number of trials is large and the probability of success is small. In this case, the number of trials is 120 and the probability of success is 0.01, so the Poisson approximation is appropriate.The mean of the Poisson distribution is equal to the product of the number of trials and the probability of success, which is 120 * 0.01 = 1.2. The probability of getting at least two wrong numbers is the complement of the probability of getting zero or one wrong number. The probability of getting zero wrong numbers is e^-1.2 = 0.301, and the probability of getting one wrong number is 1.2 * e^-1.2 = 0.361. Therefore, the probability of getting at least two wrong numbers is 1 - 0.301 - 0.361 = 0.337.

Determine the Required Probability by Using the Poisson Approximation to the Binomial