Question
Asked Oct 29, 2019
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The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time less than 3.75 minutes. (round to three decimal places)

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Expert Answer

Step 1

A uniform distribution has an equal probability for all the outcomes of the random variable, that is, it has a constant probability. A continuous uniform distribution is defined over the range (a, b) where a is the smallest value and b is the largest value of the distribution. The values (a, b), are the parameters of the uniform distribution.

Consider, X be the random variable that represents the passengers waiting time is uniformly distributed with the parameters a= 0 and b = 9.

Step 2

The probability that a randomly selected passenger has a wait...

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1 P(X 3.75)= 375 b-a 375 1 dx 9-0 1375 dx 3.75-0 = 0.417

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