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 30 seconds to 18 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? (Round your intermediate & final answers to 2 decimal places.)

a b (b-1) What is the mean time to resolve the problem? (Round your intermediate & final answer to 2 decimal places.) Mean

(b-2) What is the standard deviation of the time? (Round your intermediate & final answer to 2 decimal places.) Standard deviation

(c) What percent of the problems take more than 5 minutes to resolve? (Round your intermediate & 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? (Round your intermediate values to 2 decimal places & final answers to 3 decimal places.)

End point 1 End point 2

Explanation / Answer

a) the endpoints of the uniform distribution are a= 0.5 min and b = 18 min

b) mean = (a+b)/2 = (0.5+18) = 9.25 min

c) The formula should be in your Stat book:

standard deviation = square root [(1/12)(b - a)^2] = 5.04minutes

d) P(X > 5) = (18 - 5) / (18 - 0.5) = 0.742 or 74.2%

e) You want 50% on each side of the mean:

= mean +/- 0.50(18-0.5) = 9.25 min +/- 8.75

So, the two endpoints are:

9.25 - 8.75 = 0.5 min

9.25 + 8.75 = 18 min

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