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 0.292, then find the duration of the randomly selected class, i.e., if P(x>c)=0.292P(x>c)=0.292, then find cc, where cc is the duration of the randomly selected class. Round your answer to one decimal places.c=c= minutes

Answer 1

The duration of the randomly selected class is approximately 53.5 minutes.

Step-by-step explanation:

To find the duration of the randomly selected class, we need to find the value of 'c' where P(x > c) = 0.292. Since the duration of the class follows a continuous uniform distribution between 49.2 and 55.5 minutes, the probability that the duration is longer than a certain number of minutes is given by (55.5 - c) / (55.5 - 49.2) = 0.292. Solving this equation for 'c', we get c = 53.5321. Therefore, the duration of the randomly selected class is approximately 53.5 minutes.