5. You are waiting for your friend to their house. You density believe the wait

Question

5. You are waiting for your friend to their house. You density believe the wait time can be any number between 5 and 15 minutes, with uniform a. What is the probability that you wait less than 2.5 minutes? b. What is the expected time in minutes that you will be waiting for your friend? Interpret this in context of the problem in a sentence or two. c. What is the probability that you wait between 8 and 12 minutes? Now say you are to wait for your friend 5 days in a row, with each day being independent of one another. d. What is the probability that you wait more than 8 minutes everyday? e. What is the probability that you wait more than 2.5 minutes at least one of the days?

Explanation / Answer

P( wait less than 2.5 minutes) = 0 since wait time is distributed between 5 and 15 minutes.

b) Expected time = (5+15)/2=10 minutes. I would have to wait an average of 10 minutes for my frined.

c)P( 8 to 12 minutes) = (12-8)/(15-5)=0.4

d) P( more than 8 mintues one day) = 15-8 /[10] = 0.7

P( more than 8 minutes on 5 days] = 0.7^5=0.16807

e)P( more than 2.5 minutes on atleast one day] =0.0

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