Question

Customers experiencing technical difficulty with their Internet cable hookup may call an 800 number for technical support. It takes the technician between 108 seconds to 12.6 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

a. What are the values for a and b in minutes? (Do not round the intermediate calculations. Round the final answers to 1 decimal place.) a__ b___

b-1. What is the mean time to resolve the problem? (Do not round the intermediate calculations. Round the final answer to 2 decimal places.) Mean__

b-2. What is the standard deviation of the time? (Do not round the intermediate calculations. Round the final answer to 2 decimal places.) Standard deviation__

c. What fraction of the problems take more than 5 minutes to resolve? (Do not round the intermediate calculations. Round the final answer to 2 decimal places.) Percent %__

d. Suppose we wish to find the middle 50% of the problem-solving times. What are the end points of these two times? (Do not round the intermediate calculations. Round the final answers to 3 decimal places.) Lower end point __Upper end point____

Answer 1

a)

The distribution of this support time follows the uniform distribution.

a=108/60=1.8

b=12.6

b)

Mean time to resolve the problem :

Standard deviation :

c) Problems take more than 5 minutes to resolve

P(5<support time <12.6)= height * base

=(1/b-a)*5

=(1/(12.6-5))*5

=(1/7.6)*5

=0.1315789*5

=0.66

d) Suppose we wish to find the middle 50% of the problem-solving times.

0.5=(b-x)/(b-a)

0.5=(12.6-x)/(12.6-1.8)

0.5=(12.6-x)/10.8

12.6-x=10.8*0.5

12.6-x=5.4

x=12.6-5.4

x=7.2 Upper side end point

0.5+5.4=5.9 lower end point