Question

A postman makes a delivery every weekday (Monday to Friday) around 10 AM. The probability for the postman to be late for delivery in a certain day is 0.4.

1. What is the probability that the postman will be late on no more than 2 days during the working week (Monday to Friday)?

2. What is the probability that the postman is late for the first time on the 5th day?

3. How long until the postman is expected to be late for the 3rd time?

4. The postman has a 10 week contract for his particular delivery. If he is late more than 2 times during a week ( Mon to Fri), the client files a complaint. Upon filing 3 complaints, the company terminates the contract. What is the probability that the postman fulfills the entire contract ( less than 3 complaints during the 10 week contract)?

Please clearly explain all the steps and show them all!

Answer 1

Answers from the given data, the numbers of days that the postman is late out of the 5days here is modelled as XN Bin (0= 5, P=0.4) 9 (x – 2) - VA -0)+P(x - 1) +P(x - 2) (8) Coup (1-0.4 + (5] (0.4)(1-0. 4) + (5] 10.43² (1-0.43 -0.0778 +0.2592 +0.3456 -0.6826 (P(x c2] = 0.6826 2) the probability that the postman is late for the first time on the 5th day is to be - 7.5 poseb probability of post man not being late 'in first 4 days* probability of being late on the 5th day. (1-0.4) "*0.4 =(0.05184 3) the expected number of days fill which the postman is expected late ard time = 3/8 = 32.4 " the expected number of days (7.5 4) the probability of a complaint in any week is P(x>2) - 1-PCXS 2): 1-0.6826 = 0.3174 the probability of less than 3 complaints during the loweek Contract is PCY=0) + PCy=1) + PCY=2) = (10) (0.3174 (1.0.317430 + (10) (0-3174)' (1-0.3174) 1976-31-743 01-651249 0.022 +0.1021+0.2131 0.3378 thank your