Question

The time T (in minutes) required to perform a certain job is uniformly distributed over the interval [15; 60], which means that T is equally likely to take on any value in [15; 60] while it is impossible to take on any value outside that interval. 1 MATH 32 Worksheet 05: Chapter 5 Fall 2018 (a) Write down the probability mass function of T. (b) Find the probability that the job requires more than 30 minutes. (c) Given that the job is not nished after 30 minutes, nd the probability that the job will require more than 15 additional minutes.

Answer 1

T ~ U [15 , 60]

a) f(t) = (t - 15) / (60 - 15) = (t - 15) / 45         , 15 < t < 60

b) P(t > 30) = 1 - P(t < 30)

                   = 1 - (30 - 15) / 45

                   = 2/3 or 0.67

c) P(t > 45 | t > 30) = P(t > 45 and t > 30) / P(t > 30)

                               = P(t > 45) / P(t > 30)

                               = (1 - (45-15)/45) / (2/3)

                               = (1/3) / (2/3)

                               = 1/2 or 0.5