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 150 calls
Received by the switchboard, there are no wrong numbers.
A)0.223
B)0.335
C)0.245
D)0.777

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 150 calls
Received by the switchboard, there are no wrong numbers. 
A)0.223
B)0.335
C)0.245
D)0.777

Quizplus · Accepted Answer

The Poisson approximation is used when n is large and p is small. Here, n = 150 and p = 0.01, so λ = np = 1.5. The probability of no wrong numbers is given by P(X=0) = e^(-λ) * λ^0 / 0! = e^(-1.5), which is approximately 0.223.

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