College-Pro Painting does home interior and exterior painting. The company uses inexperienced painters that do not always do a high-quality job. It believes that its painting process can be described by a Poisson distribution with an average of 4.8 defects per 400 square feet of painting. What is the probability that a 400-square-foot painted section will have fewer than 6 blemishes?

Question

Quizplus · Accepted Answer

The Poisson probability formula is used to calculate the probability of a given number of events happening in a fixed interval of time or space. The formula is P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average number of occurrences (mean), k is the number of occurrences, and e is approximately equal to 2.71828. In this case, λ = 4.8 defects per 400 square feet. To find the probability of having fewer than 6 blemishes, we need to calculate the sum of probabilities for 0, 1, 2, 3, 4, and 5 blemishes and subtract that sum from 1. However, the correct approach is to directly calculate the cumulative probability of having 0 to 5 blemishes using a Poisson distribution calculator or table, as manually calculating each probability and summing them would be tedious. The correct answer, D) 0.6510, represents the cumulative probability of having fewer than 6 blemishes in a 400-square-foot section, according to the Poisson distribution with a mean of 4.8.

College-Pro Painting Does Home Interior and Exterior Painting