On average, Colby has noticed that 21 trains pass by his house daily (24 hours) on the nearby train tracks. What is the probability that at most 6 trains will pass his house in a 12-hour time period

10.16% probability that at most 6 trains will pass his house in a 12-hour time period

Step-by-step explanation:

We are dealing with the mean during a period of time, so we use the Poisson distribution to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

Colby has noticed that 21 trains pass by his house daily (24 hours)

We are working with 12 hour periods(half of 24), so

What is the probability that at most 6 trains will pass his house in a 12-hour time period

So

10.16% probability that at most 6 trains will pass his house in a 12-hour time period

5/12, or 5: 12

step-by-step explanation: