Problem 6BSC

Continuous Uniform Distribution. In Exercises, refer to the continuous uniform distribution depicted in Figure and described in Example. Assume that a subway passenger is randomly selected, and find the probability that the waiting time is within the given range.

Example Subway to Mets Game

For New York City weekday late-afternoon subway travel from Times Square to the Mets stadium, you can take the #7 train that leaves Times Square every 5 minutes. Given the subway departure schedule and the arrival of a passenger, the waiting time x is between 0 min and 5 min, as described by the uniform distribution depicted in Figure. Note that in Figure, waiting times can be any value between 0 min and 5 min, so it is possible to have a waiting time of 2.33457 min. Note also that all of the different possible waiting times are equally likely.

Figure Uniform Distribution of Waiting Time

Less than 0.75 minutes

Answer:

Step 1:

Given that, For New York City weekday late-afternoon subway travel from Times Square to the Mets stadium, you can take the #7 train that leaves Times Square every 5 minutes. Given the subway departure schedule and the arrival of a passenger, the waiting time x is between 0 min and 5 min, as described by the uniform distribution depicted in Figure. Note that in Figure, waiting times can be any value between 0 min and 5 min, so it is possible to have a waiting time of 2.33457 min. Note also that all of the different possible waiting times are equally likely.

Given ,

Uniform Distribution of Waiting Time

Less than 0.75 minutes.

Therefore,

The probability is the underneath the straight line (p(x) = 0.2) on the given interval.

( 0.75 - 0) 0.2 = 0.75 0.2 = 0.15.

The area of the rectangle is the product of the length and the width.