Problem 8BSC

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

Between 1.5 minutes and 4.5 minutes

Answer

Step 1 of 1 :

Continuous Uniform Distribution. The continuous uniform distribution is the probability distribution of random number selection from the continuous interval between a and b.

Given

Between 1.5 minutes and 4.5 minutes

Here a=1.5 and b=4.5

The probability is the area underneath the straight line P(x) = 0.2 on given interval:

Therefore p(x)=0.2

Area = (base) (height) p(x) = 1

Area = (b-a) (p(x)) = 1

Here we know that 1 minute and 3 minutes.

= (4.5-1.5)(0.2)

= 3 (0.2)

= 0.6

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