The time between failures for an electrical appliance is exponentially distributed with a mean of 25 months. What is the probability that the next failure will not occur before 30 months have elapsed?
A) not in excess of .2
B) in excess of .2 but not in excess of .3
C) in excess of .3 but not in excess of .4
D) in excess of .4 but not in excess of .6
E) in excess of .6

Question

The time between failures for an electrical appliance is exponentially distributed with a mean of 25 months. What is the probability that the next failure will not occur before 30 months have elapsed?
A) not in excess of .2
B) in excess of .2 but not in excess of .3
C) in excess of .3 but not in excess of .4
D) in excess of .4 but not in excess of .6
E) in excess of .6

Quizplus · Accepted Answer

The probability that the next failure will not occur before 30 months have elapsed can be calculated as:
P(X > 30) = e^(-30/25) = 0.449
This means that there is a 44.9% chance that the appliance will not fail before 30 months have elapsed. 
Since this probability is in excess of .3 but not in excess of .4, the best choice is option C.

The Time Between Failures for an Electrical Appliance Is Exponentially