Customers experiencing technical difficulty with their inter

Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds and 13 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

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

What is the mean time to resolve the problem? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

What is the standard deviation of the time? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

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.)

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.)

Solution

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
a)
b = Maximum Value = 780
a = Minimum Value = 30
b)
Mean = a + b / 2 = 405
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 216.506
c)
Normal Distribution
Mean ( u ) =405
Standard Deviation ( sd )=216.506
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

P(X > 300) = (300-405)/216.506
= -105/216.506 = -0.485
= P ( Z >-0.485) From Standard Normal Table
= 0.6862