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?
To solve this question, you can apply the concept of a uniform distribution. A uniform distribution assumes that every outcome within a given range is equally likely.
In this case, the uniform distribution ranges from 18 minutes to 26 minutes. Since we want to find the probability of a sitcom having 25 or more minutes of programming, we need to calculate the probability of selecting a value from this range that is 25 or greater.
To calculate this probability, you need to find the ratio of the interval from 25 to 26 (which represents the value of 25 or greater) to the total interval from 18 to 26.
First, let's determine the length of each interval:
Total interval: 26 - 18 = 8 minutes
Interval of interest (25 to 26): 26 - 25 = 1 minute
Now, we can calculate the probability:
Probability = (Length of interval of interest) / (Total interval)
Probability = 1 minute / 8 minutes = 1/8
Therefore, the probability that a sitcom will have 25 or more minutes of programming is 1/8 or 0.125 (12.5%).