a statistics professor plans class so carefully that the lengths of his classes are uniformly distributed between 45.0 and 55.0 minutes. find the probability that a given class period runs greater than 50.75 minutes? find the probability of selecting a class that runs greater than 50.75 minutes

If they are uniformly distributed:

(55-50.75)/10 = ?

To find the probability that a given class period runs greater than 50.75 minutes, we need to calculate the area under the probability density function (PDF) curve for the uniform distribution from 50.75 minutes to the maximum value of 55.0 minutes.

The probability density function (PDF) for a uniform distribution is defined as:

f(x) = 1 / (b - a)

where a and b are the minimum and maximum values of the distribution, respectively.

In this case, a = 45.0 minutes and b = 55.0 minutes.

To find the probability, we need to determine the area under the curve between 50.75 minutes and 55.0 minutes. Since the PDF for a uniform distribution is constant within its range, the area under the curve is simply the width of the interval divided by the total width of the distribution:

P(X > 50.75) = (55.0 - 50.75) / (55.0 - 45.0)

P(X > 50.75) = 4.25 / 10

P(X > 50.75) = 0.425

Therefore, the probability that a given class period runs greater than 50.75 minutes is 0.425, or 42.5%.

To find the probability of selecting a class that runs greater than 50.75 minutes, we can assume that each class has an equal chance of being selected. Since all classes have the same probability of exceeding 50.75 minutes, the probability remains the same as calculated above, which is 0.425 or 42.5%.