Question

My employee seems to leave work anytime between 4PM and 5PM, uniformly.

a) What is the probability he will still be at work at 4:20 ​PM?​

b) What is the probability he will still be at work at 4:20 PM every day this week ​(M–​F)?

​c) What did you assume to calculate​ b?

Answer 1

The distribution of the time of stay after 4 pm here is given as:

in minutes.

a) Probability that he will still be at work after 420 pm is computed here as:

Therefore 2/3 = 0.6667 is the required probability here.

b) The probability that the same scenario as above is repeated on all 5 days is computed here as:

Therefore 0.1317 is the required probability here.

c) The assumption in part b) here is that for all 5 days the time of work is independent of each other. Therefore the probability that he still work until 420 pm wont have an effect on the probability in the next 4 days.