In 2015, Oklahoma experienced 907 perceptible earthquakes (far surpassing California), for an average of about 2.5 perceptible earthquakes per day. Consider perceptible earthquakes that occur independently with a constant daily rate of 2.5. (Enter all your answers rounded to four decimal places.)

(a) What is the probability P of a day with no perceptible earthquakes?

The probability P of a day with no perceptible earthquakes is 0.0821.

Step-by-step explanation:

We will consider that earthquakes occurring in a day is a Poisson process. The following Poisson probability distribution formula will be used in this question.

p (x,λ) = [e^-λ (λ) ˣ]/x!

where x = number of outcomes occurring

λ = mean number of occurrences

(a) So, in this question we have λ = 2.5 and we need to find the probability that x=0 (no perceptible earthquakes in a day). So,

P (X=0) = p (0,2.5) = [ (e^-2.5) (2.5) ⁰]/0!

= ((0.0821) * 1) / 1

P (X=0) = 0.0821

The probability P of a day with no perceptible earthquakes is 0.0821.