The time between arrivals of small aircraft at a county

Chapter 4, Problem 126E

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QUESTION:

Problem 126E

The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour.

(a) What is the probability that more than three aircraft arrive within an hour?

(b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals?

(c) Determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.10.

Questions & Answers

QUESTION:

Problem 126E

The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour.

(a) What is the probability that more than three aircraft arrive within an hour?

(b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals?

(c) Determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.10.

ANSWER:

Solution:

Step 1 of 4:

The time interval between the arrivals of an aircraft is exponentially distributed with a mean of one hour.

  1. We have to find the probability that more than three aircraft arrive within an hour.

  1. We have to find the probability that no interval contains more than three arrivals, if 30 separate one-hour intervals are chosen.

  1. We have to find the length of an interval of time, if the probability that no arrivals occur during the interval is 0.10.


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