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A plumber tells you she will arrive between 8 am and noon. Assume any time in this interval
is an equally likely arrival time. Let X= arrival time (minutes after 8 am).
State the distribution that X follows in proper mathematical notation.
(a) Find the probability density function f(x) and sketch a graph of it in your notes.
(b) What is the probability she arrives before 9 am?
Pose this question with mathematical notation and compute the answer.
(c) What is the probability she arrives between 10:15 and 11 am?
Pose this question with mathematical notation and compute the answer.
(d) It is now 9:30. What is the probability that she arrives in the next 30 minutes?
Pose this question with mathematical notation and compute the answer.
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This probability distribution as described in the problem, is called a UNIFORM distribution.
(a) Find the probability density function f(x) and sketch a graph of it in your notes.
The formula for the density distribution is f( x ) = = constant.
Here x represents any ONE minute time interval after 8 am;
240 represents 4 hours from 8 am to noon in minutes, 240 = 60 minutes * 4 hours.
(b) What is the probability she arrives before 9 am?
Pose this question with mathematical notation and compute the answer.
P(x <= 9 am) = = ,
saying that the probability to arrive between 8 am and 9 am is 1/4.
(c) What is the probability she arrives between 10:15 and 11 am?
Pose this question with mathematical notation and compute the answer.
P(10:15 am x <= 11 am) = = ,
saying that the probability to arrive between 10:15 am and 11:00 am is 3/16.
(d) It is now 9:30. What is the probability that she arrives in the next 30 minutes?
Pose this question with mathematical notation and compute the answer.
P(x <= 30 minutes given that it is 9:30 now) = = ,
saying that the probability to arrive next 30 minutes given that it is 9:30 now
is 1/5.
It is BECAUSE there are only 2 hours 30 minutes, or 150 minutes, from now till noon.
At this point, the problem is solved in full - I answered all questions,
having provided you all necessary explanations.