Question

Customers experiencing technical difficulty with their Internet cable service may call an 800 number for technical support. It takes the technician between 30 seconds and 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

3. What percent of the problems take more than 5 minutes to resolve? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

4. 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 intermediate calculations. Round your answers to 3 decimal places.)

Answer 1

ANSWER

a = 30 seconds = 0.5 minutes
b = 10 minutes

Mean = (a+b)/2 = (0.5+10)/2 = 10.5/2 = 5.25 minutes

Mean=5.25 minutes
sd = sqrt((b-a)^2/12) = sqrt((10-0.5)^2/12)

=sqrt((9.5^2/12))

=sqrt(90.25/12)

=sqrt(7.520)

= 2.7424 minutes

  

=> percent of the problems take more than 5 minutes to resolve = (b-x)/(b-a)
= (10-5)/(10-0.5)
= 5/9.5
= 0.5263
= 52.63%

=> 0.25 = (b-x)/(b-a)

=(10-x)/(10-0.5)

0.25 = (10-x)/9.5

Multiply by 9.5:

10 - x = 2.375

x = 10-2.375

x = 7.625  

The upper side = 7.625

Lower side = 0.5+2.375

Lower side = 2.875

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