Question

Let X, the number of flaws on the surface of a randomly selected boiler of a certain type, have a Poisson distribution with parameter μ = 5. Use the cumulative Poisson probabilities from the Appendix Tables to compute the following probabilities. (Round your answers to three decimal places.)(a) P(X ≤ 8)(b) P(X = 8)(c) P(9 ≤ X)(d) P(5 ≤ X ≤ 8)(e) P(5 < X < 8)

Answer 1

Answer:

(a) 0.932

(b) 0.0653

(c) 0.032

(d) 0.316

(e) 0.251

Step-by-step explanation:

From the table with mean parameter μ = 5, we can compute the following cumulative and density probability

(a) $P(X \leq 8) = 0.932$ (cumulative)

(b) P(X = 8) = 0.0653 (density)

(c) $P(9 \leq X) = 1 - P(X \leq 9) = 1 - 0.968 = 0.032$ (cumulative)

(d) $P(5 \leq X \leq 8) = P(X \leq 8) - P(X \leq 5) = 0.932 - 0.616 = 0.316$ (cumulative)

(e) $P(5 < X < 8) = P(X \leq 8) - P(X \leq 5) - P(X = 8) = 0.932 - 0.616 - 0.0653 = 0.251$