Question

A subway train on the Red Line arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.

a. Define the random variable. X = _______


b. X ~ _______


c. Graph the probability distribution.


d. f(x) = _______


e. μ = _______


f. σ = _______


g. Find the probability that the commuter waits less than one minute.


h. Find the probability that the commuter waits between three and four minutes.


i. Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probability.

Answer 1

The random variable is the length of time a commuter must wait for a train to arrive on the Red Line. The probability distribution can be graphed as a horizontal line with a height of 1/8 for 0 ≤ x ≤ 8. The probability that the commuter waits less than one minute is 1/8.

Step-by-step explanation:

a. X represents the length of time a commuter must wait for a train to arrive on the Red Line.
b. X ~ U(0,8)
c. The probability distribution can be graphed as a horizontal line with a height of 1/8 for 0 ≤ x ≤ 8.
d. f(x) = 1/8 for 0 ≤ x ≤ 8
e. μ = 4
f. σ = 2.309
g. To find the probability that the commuter waits less than one minute, we can calculate the area under the probability distribution curve from 0 to 1. This can be done by finding the area of a rectangle with height 1/8 and width 1.
h. To find the probability that the commuter waits between three and four minutes, we can calculate the area under the probability distribution curve from 3 to 4. This can be done by finding the area of a rectangle with height 1/8 and width 1.
i. To find the length of time where sixty percent of commuters wait more than, we need to find the value x such that the area under the probability distribution curve to the right of x is 0.6. This can be done by finding the value x such that the area of the rectangle to the right of x is 0.6.