Question

Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 18 seconds and 13 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

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.)

Answer 1

Solution:

Given: x = the technician resolve the problem follows the uniform distribution between 18 seconds and 13 minutes.

18 seconds = 18/60 = 0.3 minutes

thus a = 0.3 minutes and b = 13 minutes.

Thus X ~ Uniform(a = 0.3 , b = 13)

We have to find end-points of  the middle 50% of the problem-solving times.

Middle 50% of the data is between first quartile Q₁ and third quartile Q₃.

Thus we have to find:

P( Q₁ < X < Q₃ ) =50%

Since 25% of the data is below Q₁, we use:

P( X < Q₁) = 25%

P( X < Q₁) = 0.25

and 75% of the data is below Q₃, we use:

P( X < Q₃) = 75%

P( X < Q₃) = 0.75

Using cumulative distribution function of Uniform distribution:

Thus

and

Thus end points are:   and .

That is middle 50% of the data is between 3.475 and 9.300