Mr. Cotton has to give a lecture at 3:30. From past experience, we know that Mr.

Question

Mr. Cotton has to give a lecture at 3:30. From past experience, we know that Mr. Cotton will arrive from 1 minute early up to 5 minutes late and is equally likely to arrive at any of these times (So it's uniformly distributed). He will begin the lecture 2 minutes after he arrives 3. (a) What is the probability that Mr. Cotton begins the lecture after 3:351 (b) What is the expected time that the lecture will begin? (c) What is the standard deviation, in minutes, for the time that the lecture begins?

Explanation / Answer

here time is unifomely distribution from 3:29 to 3:35 which can be converted from 0 to 6 minute where a=0 referes 3:29 and b=6 refers to 3:35

a) probability that lecture begins after 3:35 =P(X>6) =0 (as professor can be late at most 5 minute not more then that)

b) expected time =(a+b)/2 =(0+6)/2 =3 minute which is equivalent to 3:32

c) std deviaiton =(b-a)/(12)1/2 =(6-0)/(12)1/2 =1.7321

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