Question

Solve the following problems using Poison Probability distribution If 3 percent of all the cars fail the emission inspection, find the probability that in a sample of 90 cars, 3 will fail.

Answer 1

To solve the problem, use the Poisson Probability distribution and calculate the mean (average) number of cars that fail the inspection in a sample of 90 cars. Then, use the Poisson probability formula to find the probability that at most four cars will fail.

Step-by-step explanation:

To solve this problem using the Poisson Probability distribution, we need to first calculate the mean (average) number of cars that fail the inspection in a sample of 90 cars. To do this, we multiply the percentage of cars that fail by the total number of cars in the sample:

Mean (average) = 3% x 90 cars = 0.03 x 90 cars = 2.7 cars

Next, we use the Poisson probability formula to find the probability that at most four cars will fail:

P(X ≤ 4) = e^(-λ) * (λ^x) / x!

Where λ is the mean (average) number of events occurring in a given interval, x is the number of events we want to find the probability for, and e is the mathematical constant approximately equal to 2.71828.

Using λ = 2.7 and x = 4, we can calculate the probability:

P(X ≤ 4) = e^(-2.7) * (2.7^4) / 4!

P(X ≤ 4) = 0.065