Question

The mean number of visitors at a national park in one weekend is 52. Assume the variable follows a poisson distribution. Find the probability that there will be 58 visitors at this park in one weekend. That is, find P(X=58)

Answer 1

To find the probability that there will be 58 visitors at the national park in one weekend, we can use the Poisson distribution formula. The probability is approximately 0.0948, or 9.48%.

Step-by-step explanation:

To find the probability that there will be 58 visitors at the national park in one weekend, we can use the Poisson distribution formula. The formula for the probability mass function of a Poisson distribution is P(X=k) = (e^(-λ) * λ^k) / k!, where λ is the mean number of visitors. In this case, λ = 52. Plugging in the values, we get P(X=58) = (e^(-52) * 52^58) / 58!. By evaluating this expression, the probability is approximately 0.0948, or 9.48%.

Answer 2

0.0374722

Step-by-step explanation:

Given that :

μ = 52

x = 58

P(x, μ) = (e^-μ) * (μ^x)/ x!

P(58, 52) = ((e^-52) * (52^58)) / 58!

P(58, 52) = [(2.6102E−23 * 3.37437E99) / 2.35056E78]

P(58, 52) = 8.80807E76 / 2.35056E78

P(58, 52) = 0.0374722