Question

A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X= the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is ... What is the probability that the lecture continues beyond the hour for between 60 and 90 sec?

Answer 1

The probability that the lecture continues beyond the hour for between 60 and 90 seconds is 0.25 or 25%.

Step-by-step explanation:

The given problem is asking for the probability that the lecture continues beyond the hour for between 60 and 90 seconds. We can solve this problem by finding the probability that X, the time that elapses between the end of the hour and the end of the lecture, is between 60 and 90 seconds. Since X is uniformly distributed between 0 and 120 seconds, we can find the probability by calculating the area under the probability density function (pdf) curve for X between 60 and 90 seconds.

The pdf of a uniform distribution is given by:

f(x) = 1/(b-a), for a ≤ x ≤ b

where a and b are the lower and upper bounds of the distribution. In this case, a = 0 seconds and b = 120 seconds.

So, the probability that X is between 60 and 90 seconds is:

P(60 ≤ X ≤ 90) = (90 - 60)/(120 - 0) = 30/120 = 0.25 or 25%