Question

If a variable x follows a Poisson distribution with an average (μ) of 3, what is the probability that x is equal to 5? Please round the probability to four decimal places.

Answer 1

The probability that a variable x follows a Poisson distribution with a mean of 3 and is equal to 5, is approximately 0.1008 when rounded to four decimal places.

Step-by-step explanation:

When variable x follows a Poisson distribution with a mean (μ) of 3, the formula we use to calculate the probability of x being a specific value is given by:

P(x) = μ^x * e^(-μ) / x!

For x = 5:

• μ (mean) = 3
• e (Euler's number) ≈ 2.71828

The probability that x is equal to 5 is calculated as follows:

P(5) = 3^5 * e^(-3) / 5! = 243 * e^(-3) / 120 ≈ 243 * 0.04979 / 120 = 0.10082

Rounded to four decimal places:

P(x = 5) ≈

0.1008