Question

Assume the Poisson distribution applies. Use the given mean to find the indicated probability.

Find ​P(5​) when μ = 9

Answer 1

Answer: 0.155

Explanation:

To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:

P(k) = (μ^k * e^(-μ)) / k!

Where:

• P(k) is the probability of the event occurring k times
• μ is the mean
• e is the base of the natural logarithm ( approximately 2.71828)
• k! is the factorial of k (k factorial)

Plugging in the given values, we get:

P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550

So the probability of the event occurring 5 times is approximately 15.5%.