SOLUTION: 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

Algebra ->  Probability-and-statistics -> SOLUTION: 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      Log On


   

Question 1206029: 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.

Find the probability density function f(x) and sketch a graph of it in your notes.

What is the probability she arrives before 9 am? Pose this question with mathematical notation and compute the answer.

What is the probability she arrives between 10:15 and 11 am? Pose this question with mathematical notation and compute the answer.

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.
Answer by ikleyn(53646) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~ 


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 ) = 1%2F240 = 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) = 60%2F240 = 1%2F4, 

     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) = 45%2F240 = 3%2F16, 

     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) = 30%2F150 = 1%2F5, 

     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.