The time between arrivals of small aircraft at a county airport is exponentially

Question

The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places (e.g. 98.765). What is the probability that more than three aircraft arrive within an hour? If 30 separate one-hour intervals are chosen, what Is the probability that no interval contains more than three arrivals? Determine the length of an interval of time (In hours) such that the probability that no arrivals occur during the interval is 0.14.

Explanation / Answer

Answer to part c)

We got that the probability that no arrival takes place between a specific time interval is 0.14

We do not know the time interval

We integrate the values from 0 to x and get

e^-x = 0.14

Like this we get x ~ 2 hours

thus the correct answer to part c is : 2 hours

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