Question

Assume that X is a Poisson random variable with μ= 6. Calculate the following probabilities. (Round your intermediate calculations and final answers to 4 decimal places.)

P(X = 5)

Answer 1

To calculate the probability that X equals 5 in a Poisson distribution with a mean of 6, we use the Poisson probability formula.

Step-by-step explanation:

To calculate the probability that X equals 5 in a Poisson distribution with a mean of 6, we can use the Poisson probability formula. The formula is P(X = k) = e^(-μ) * (μ^k) / k!. In this case, μ is 6 and k is 5. Plugging these values into the formula, we get:

P(X = 5) = e^(-6) * (6^5) / 5!

This can be further simplified to: P(X = 5) ≈ 0.1606