Suppose you are at the airport waiting to receive your friend. The announcement

Question

Suppose you are at the airport waiting to receive your friend. The announcement says that the flight is expected to land in another 20 minutes. Mentally you are curious with the following questions, depending on various scenarios. 1. What is the probability that the flight lands in between now and the next 10 minutes? (A situation that you are excited and want to see your friend as early as possible) 2. What is the probability that the flight lands in between the 15th and 20th minute? 3. Find the mean and standard deviation of the distribution

Explanation / Answer

Solution:

1) The interval of the probability distribution in minutes is [0, 20].
And the probability density is
1 / (20–0) = 1 / 20.
You wish your friend to land within next 10 minutes. That is, the sub interval of the successful event is [0, 10]. Now the probability P ( x < 10) is the ratio of the widths of these two intervals.
=> 10/ 20 =1 /2
2) The interval of the probability distribution in minutes is same as [0, 20].
=> The probability density is = 1/20–0 = 1/20.

You wish your friend to land in the last 5 minutes. That is, the sub interval of the successful event is [0, 5].
Now the probability P (15 < x < 20) is the ratio of the widths of these two intervals.
=> 5/20=1/4

Hence, the probability of the flight landing within 5 minutes is 1/4.

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