On average, 30-minute television sitcoms have 22 minutes of...

On average, 30-minute television sitcoms have 22 minutes of programming (CNBC, February $23,2006 ) .$ Assume that the probability distribution for minutes of programming can be approximated by a uniform distribution from 18 minutes to 26 minutes. a. What is the probability that a sitcom will have 25 or more minutes of programming? b. What is the probability that a sitcom will have between 21 and 25 minutes of programming? c. What is the probability that a sitcom will have more than 10 minutes of commercials or other nonprogramming interruptions?

On average, 30-minute television sitcoms have 22 minutes of programming (CNBC,
February $23,2006 ) .$ Assume that the probability distribution for minutes of programming
can be approximated by a uniform distribution from 18 minutes to 26 minutes.
a. What is the probability that a sitcom will have 25 or more minutes of programming?
b. What is the probability that a sitcom will have between 21 and 25 minutes of
programming?
c. What is the probability that a sitcom will have more than 10 minutes of commercials
or other nonprogramming interruptions?

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Key Concepts

Probability Calculation in Uniform Distributions

For a uniform distribution defined over an interval, the probability that the random variable falls within a certain range is determined by the ratio of the length of that range (support) to the total length of the distribution's interval. This method allows for an instantaneous computation of probabilities without complex integration.

Uniform Distribution

A uniform distribution is a continuous probability distribution in which all intervals of the same length within the distribution’s range have an equal probability of occurring. Its properties facilitate the straightforward calculation of probabilities over any interval by simply comparing the length of the subinterval of interest to the total interval length.

Transformation Between Related Variables

When two variables are linked through a fixed total (such as programming time and nonprogramming time in a television show), understanding this connection allows one to convert probabilities from one domain to another. This transformation is useful when the question requires probabilities about a component that is defined as a difference from a total.

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