Question

Suppose a random variable, x, follows a Poisson distribution. Let μ = 2.5 every minute, find the P(X ≥ 125) over an hour. Round answer to 4 decimal places.

Answer 1

To find the probability P(X ≥ 125) over an hour, we convert the mean from minutes to hours and use the Poisson probability formula.

Step-by-step explanation:

To find the probability P(X ≥ 125) over an hour, we need to convert the given mean from minutes to hours. Since μ = 2.5 every minute, in an hour, μ = 2.5 * 60 = 150.

Next, we can use the Poisson probability formula to calculate P(X ≥ 125) over an hour.

P(X = k) = (e^(-μ) * μ^k) / k!, where e is the base of natural logarithm.

P(X ≥ 125) = 1 - P(X < 125).

Using the formula, we can calculate the probability P(X = 124) and subtract it from 1 to get the result.