A book contains 500 pages. If there are 200 typing errors randomly distributed throughout the book, use the Poisson distribution to determine the probability that a page contains exactly two errors.
A)0.0536
B)0.0108
C)0.4423
D)0.0893

Question

Quizplus · Accepted Answer

We are given that the Poisson distribution applies and we can use the formula:

P(X = k) = (e^-λ * λ^k) / k!

where λ is the mean and equal to the total number of errors divided by the number of pages:

λ = 200 / 500 = 0.4

We want to find the probability that a page contains exactly two errors, so we set k = 2:

P(X = 2) = (e^-0.4 * 0.4^2) / 2! = 0.0536

Therefore, the answer is A) 0.0536. We can use the Poisson probability function given by:

P(X = k) = e^(-λ) * λ^k / k!

where X is the random variable (number of errors on a given page), k is the specific value of X we are interested in (2), and λ is the expected value of X (the average number of errors per page).

To find λ, we can divide the total number of errors by the total number of pages:

λ = 200 / 500 = 0.4

Now we can plug in these values:

P(X = 2) = e^(-0.4) * 0.4^2 / 2! = 0.0536

Therefore, the probability that a page contains exactly two errors is 0.0536 or approximately 5.36%.

A Book Contains 500 Pages