Question

The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution from 29 to 42 minutes. Let   X   denote the time until the next bus departs.

1. (3%) The distribution is    (pick one) ExponentialPoissonNormalUniform and is    (pick one) discretecontinuous .
2. 
   
3. 
   
4. 
   
5. (3%) The density function for   X   is given by   f(x)=      , with    ≤X≤    .
6. 
   
7. 
   
8. 
   
9. (3%) The mean of the distribution is
   

   μ=   .

10. 
    
11. 
    
12. 
    
13. (3%) The standard deviation of the distribution is
    

    σ=   .

14. 
    
15. 
    
16. 
    
17. (3%) The probability that the time until the next bus departs is between 30 and 40 minutes is
    

    P(30<X<40)=   .

18. 
    
19. 
    
20. 
    
21. (3%) Ninety percent of the time, the time to the next departure is less than how many minutes?
    

    That is, P(X≤k)=0.9   for   k=   .

Answer 1

We are given a uniform distribution here as:

a) It is already given in the problem that it is a uniform distribution.

b) For the given uniform distribution , the PDF for X here is obtained as:

This is the required PDF for X here.

c) The mean of the distribution is computed here as:

Therefore 35.5 is the required mean here.

d) The standard deviation here is computed as:

e) The probability here is computed as:

Therefore 10/13 is the required probability here.

f) Let the time required here be K.

Then, we have here:
P(X < k) = 0.9

Therefore 40.7 is the required value here.