Question

n an amusement park, the bumper cars are sometimes becoming disabled and in need of repair. The repairman can fix the disabled bumper cars in an average time of 20 minutes with a standard deviation of 20 minutes. Cars tend to break down at two per hour between two consecutive breakdowns following an exponential distribution. What is the total time for a disabled bumper car to be fixed

Answer 1

1 hour 20 minutes

Explanation:

Time to fix car ( repair time ) = 20 minutes

Breakdown rate ( λ ) = 2 car per hour

first step : determine service the service rate ( μ )

= 60 minutes / 20 minutes

= 3 cars per hour

next : determine the average waiting time for a disabled car

= 1 / (μ - λ)

= 1 / service rate - breakdown rate

= 1 / ( 3 - 2 )

= 1 / 1 = 1 hour

Finally Total time for a disabled car to be fixed

= repair time + average waiting time

= 20 minutes + 60 minutes

= 1 hour 20 minutes