SUPPOSE YOU HAVE A SERVICE TECHNICIAN COME TO YOUR HOME AT 10 A.M. TO LOOK AT AN ISSUE IN YOUR TELEVISION AND YOU NEED TO WATCH YOUR MOVIE WITH NO INTERRUPTIONS. AFTER A QUICK INSPECTION OF THE PROBLEM, THE TECHNICIAN TELL YOU THAT HE EXPECTS THE FIX TO TAKE ABOUT 1 HOUR. SINCE WE DONT KNOW ANYTHING ELSE ABOUT THE DISTRIBUTION OF RAPAIR TIMES, ASSUME REPAIR TIMES FOLLOW AN EXPONENTIAL DISTRIBUTION.
1. IF YOUR FAVORITE FLICK STARTS AT 10:30, WHAT IS THE LIKELIHOOD THAT THE TECHNICIAN IS FINISHED BY THEN?
A. 98.91% B. 39.35% C. 53.33% D. 73.99%
2. HOW LIKELY IS IT THAT THE REPAIR TAKES LONGER THAN 3 HOURS?
A. 13.08% B. 66.01% C.4.98% D. 88.24%
β =1 Hour
1)
P(THE TECHNICIAN IS FINISHED BY THEN in 0.5 hour):
| probability = | P(X<0.5)= | 1-exp(-0.5/1)= | 0.3935 ~ 39.35 % | |||
option B is correct
2)
| probability = | P(X>3)= | 1-P(X<3)= | 1-(1-exp(-3/1))= | 0.0498~ 4.98% | ||
option C is correct
SUPPOSE YOU HAVE A SERVICE TECHNICIAN COME TO YOUR HOME AT 10 A.M. TO LOOK AT AN ISSUE IN YOUR TELEVISION AND YOU NEED T...