Question

Customers are serviced at a rate of six customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 20​ minutes? A. Greater than 0.70 but less than or equal to 0.80 B. Greater than 0.90 C. Less than or equal to 0.70 D. Greater than 0.80 but less than or equal to 0.90.   

Please show all work

Answer 1

service rate (u) = 6/hour

20 mins = 20/60 = 0.3 hour

Probability that the time taken is less than 20 mins = 1 - e^-6*0.3

= 1 - e^-1.8

= 1 - 0.1653

= 0.8347

Ans is option D, Greater than 0.80 but less than or equal to 0.90.