On average, 30-minute television sitcoms have 22 minutes of programming.If a probability distribution for minutes of programming can be approximated by a uniform distribution from 18 minutes to 26 minutes. What is the probability a sitcom will have 25 or more minutes of programming?

2/(26-18) = ?

.25

To find the probability that a sitcom will have 25 or more minutes of programming, we first need to calculate the total probability of the uniform distribution from 18 minutes to 26 minutes.

The range of possible minutes for the sitcom programming is from 18 to 26 minutes. Since the distribution is assumed to be uniform, the probability density function (PDF) is constant within this range.

To find the constant value of the PDF, we need to calculate the total area under the PDF curve, which represents the total probability.

The total probability (area under the curve) of a uniform distribution is equal to the height of the rectangle (constant PDF value) multiplied by the width of the interval (range of minutes).

The height of the rectangle (constant PDF value) can be calculated by dividing 1 (total probability) by the width of the interval:

Height of rectangle = 1 / (26 - 18) = 1/8

Now, we can find the probability of having 25 or more minutes of programming by calculating the area under the curve for that range.

The width of the range from 25 to 26 minutes is 1 minute. So, the probability of having 25 or more minutes of programming can be calculated by multiplying the height of the rectangle by the width:

Probability = Height of rectangle * Width of interval = (1/8) * 1 = 1/8

Therefore, the probability that a sitcom will have 25 or more minutes of programming is 1/8.

To find the probability that a sitcom will have 25 or more minutes of programming, we need to calculate the probability density function (PDF) and integrate it over the interval from 25 to 26 minutes.

Since the given probability distribution can be approximated by a uniform distribution, we know that the PDF is a constant value over the entire range of 18 to 26 minutes.

To find this constant value, we need to calculate the total probability over the entire range and divide it by the range width. In this case, the range width is 26 - 18 = 8 minutes.

The total probability over the range is simply equal to 1 (or 100%).

So, the PDF value is 1 / 8 = 0.125.

Now, we can calculate the probability of having 25 or more minutes of programming by integrating the PDF from 25 to 26 minutes.

The integral of a constant value over this range is simply the value of the constant times the width of the range.

Therefore, the probability P(25 or more minutes) = (0.125) * (1) = 0.125 or 12.5%.