Question

the duration of a professor's class has continuous uniform distribution between 49.2 minutes and 55.5 minutes. if one class is randomly selected and the probability that the duration of the class is longer than a certain number of minutes is 0.532, then find the duration of the randomly selected class, i.e., if , then find , where is the duration of the randomly selected class. round your answer to one decimal places.

Answer 1

To find the duration of the randomly selected class, set up an equation where 1 - ((x - 49.2) / (55.5 - 49.2)) = 0.532 and solve for x.

Step-by-step explanation:

To find the duration of the randomly selected class, we need to determine the value of x that satisfies the condition that the probability of the class duration being longer than x is 0.532. The duration of the class has a continuous uniform distribution between 49.2 minutes and 55.5 minutes.

Since the distribution is uniform, the probability of the class duration being longer than x is equal to 1 minus the probability of the class duration being less than or equal to x. Therefore, we can write the equation:

1 - ((x - 49.2) / (55.5 - 49.2)) = 0.532

Solving this equation will give us the value of x, which represents the duration of the randomly selected class.