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.
