Question

Bill needs to schedule a meeting for tomorrow afternoon, but he also has a tee time for golf at 10:00 a.m. Bill usually finishes a round of golf in 4.25 hours. If the course is empty and he doesn’t spend too much time looking for lost balls, he can finish in 3.25 hours. However, if the course is crowded, there are rain delays, and/or he hits many bad shots, a round can take as much as 5.5 hours. a. What is the expected time that Bill will require to complete his round of golf tomorrow?(Round your answer to 2 decimal places) b. If Bill schedules a meeting to begin at 3:30 p.m. tomorrow and it takes 30 minutes for him to get from the golf course to his office, what is the probability that he will make it to the meeting on time? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Answer 1

Given,

Bill's most probable time of finish- m = 4.25 hours

Bill's optimistic time of finish - w = 3.25 hours

Bill's pessimistic time of finish - b= 5.5 hours

a) Bill's Expected time to finish golf tomorrow = (4m + w + b)/ 6 = (4*4.25 + 3.25 + 5.5)/ 6

= 4.29 hours

b) Probability for Bill to make it to Office by 3:30 pm

Target completion time = 10 am to 3 pm ( as 30 minutes are taken to reach office ) = 5 hours

Variance = [(w-b)/ 6] ²

= (3.25 - 5.5)²/ 36

= 5.0625/36 = 0.14

Thus,

Probability (z) = (Target completion time - Expected time)/ (Variance)^1/2

= (5-4.29)/ (0.14)^1/2

= 1.8975

Finding probability for same from z tables,

Probability that Bill makes to meeting in time = 0.971119 or 97%