In a Certain Very Large City, the Department of Transportation

question 5

Essay

In a certain very large city, the Department of Transportation (D.O.T.) has organized a complex system of bus transportation. In an advertising campaign, citizens are encouraged to use the new "GO-D.O.T!" system and head for the nearest bus stop to be transported to and from the central city. Suppose that at one of the bus stops the amount of time (in minutes) that a commuter must wait for a bus is a uniformly distributed random variable, T. The values of T run from 0 minutes to 30 minutes.
a) Sketch the probability distribution of T.
b) What is the probability that a random commuter will spend more than 12 minutes waiting for GO-D.O.T?

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Definitions:

Variance Accounted

A measure of the proportion of the total variance in a dataset that is explained or accounted for by a statistical model or factor.

Correlation

A numerical indicator that reveals the degree to which two factors vary in tandem, showcasing the intensity and orientation of their association.

Correlation Coefficient

A measure that indicates the extent to which two variables change together, but not necessarily at the same rate.

Test Statistic

A quantity derived from sample data that is used in a hypothesis test to determine whether to reject the null hypothesis.