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 13 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.) 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 times? (Do not round your intermediate calculations. Round your answers to 3 decimal points of these two places.) End point1 End point 2

Explanation / Answer

a)

As it is from 90 s to 13 minutes, and 90 s = 1.5 min, then

a = 1.5
b = 13 [ANSWER]

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b-1)

Note that here,          
          
a = lower fence of the distribution =    1.5      
b = upper fence of the distribution =    13      
          
Thus, the mean, variance, and standard deviations are          
          
u = mean = (b + a)/2 =    7.25   [ANSWER]

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b-2.

As
  
s^2 = variance = (b -a)^2 / 12 =    11.02083333  
Then
  
s = standard deviation = sqrt(s^2) =    3.319764048 [ANSWER]

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c)

Note that here,          
          
a = lower fence of the distribution =    1.5      
b = upper fence of the distribution =    13      
          
          
Note that P(x>c) = P(c<x<b) = (b-c)/(b-a). Thus, as          
          
c = critical value =    5      
          
Then          
          
P(x>c) =    0.695652174   [ANSWER]

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d)

We refer to the 25th and 75th percentiles here.

LOWER ENDPOINT:

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 =    13      
          
Then          
          
c = critical value =    4.375   [ANSWER, END POINT 1]

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UPPER ENDPOINT:

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 =    13      
          
Then          
          
c = critical value =    10.125   [ANSWER, ENDPOINT 2]  
  
  
      

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