Customers experiencing technical difficulty with their internet cable hookup may

Question

Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 90 seconds and 14 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 your intermediate calculations. Round your answers to 1 decimal place.) a b b-1. What is the mean time to resolve the problem? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Mean b-2. What is the standard deviation of the time? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Standard deviation c. What percent of the problems take more than 5 minutes to resolve? (Do not round your intermediate calculations. Round your 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 your intermediate calculations. Round your answers to 3 decimal places.) End point 1 End point 2

Explanation / Answer

a)

Note that 90 s = 1.5 min. Hence,

a = 1.5 [ANSWER]
b = 14 [ANSWER]

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b-1)

Note that here,          
          
a = lower fence of the distribution =    1.5      
b = upper fence of the distribution =    14      
          
Thus, the mean, variance, and standard deviations are          
          
u = mean = (b + a)/2 =    7.75 minutes   [ANSWER]  

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b-2)

Also,

s^2 = variance = (b -a)^2 / 12 =    13.02083333  
Hence,
  
s = standard deviation = sqrt(s^2) =    3.608439182   [ANSWER]

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c.

Note that here,          
          
a = lower fence of the distribution =    1.5      
b = upper fence of the distribution =    14      
          
          
Note that P(x>c) = P(c<x<b) = (b-c)/(b-a). Thus, as          
          
c = critical value =    5      
          
Then          
          
P(x>c) =    0.72   = 72% [ANSWER]

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d)

These then correspond to left tailed areas of 0.25 and 0.75.

FOR LOWER END:

Here, the left tailed area is          
          
P(x<c) =    0.25      
          
Thus, the critical value is given by          
          
c = critical value = (b-a)*P(x<c) + a =           
          
As          
          
a = lower fence =    1.5      
b = upper fence =    14      
          
Then          
          
c = critical value =    4.625      

FOR UPPER END:

Here, the left tailed area is          
          
P(x<c) =    0.75      
          
Thus, the critical value is given by          
          
c = critical value = (b-a)*P(x<c) + a =           
          
As          
          
a = lower fence =    1.5      
b = upper fence =    14      
          
Then          
          
c = critical value =    10.875      

Hence, it is between 4.625 AND 10.875. [ANSWER]  
  

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