Question

Problem 15S-1

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 4.45 hours. If the course is empty and he doesn’t spend too much time looking for lost balls, he can finish in 3.45 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 5.70 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 03:30 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

a)

Answer: Expected time that Bill will require to complete his round of golf tomorrow is 4.49 hours (or 4 hours 29.5 minutes).

b)

Answer: Probability that Bill will make it to the meeting on time is 91%.

Explanation:

a)

Most likely time (m) = 4.45 hours

Pessimistic time(b) = 5.70 hours

Optimistic time(a) = 3.45 hours

Expected time is given by (T_e)

=(3.45+4*4.45+5.70)/6

=4.4917 hours

=4.4917*60 hours

=269.5 minutes

=4 hours 29.5 minutes

b)

Standard deviation of time() =(b-a) / 6

=(5.70-3.45)/6

=0.375 hours

=22.5 minutes

Now, meeting time =3.30 pm

Considering 30 minutes for travel,

target completion time = 3:30-10:00-00:30 = 5 hours

Z=(Target completion time - mean completion time)/

=(5-4.49)/0.375

=1.36

P(Z<1.36)=0.9131

= 91%