Question

q1: New Million Car Service Centre finds that the amount of time a technician needs to fix a wheel bearing problem is between 1.5 and 4.0 hours. We are interested with the time needed to fix a wheel bearing problem.

For the following situation, suggest the most appropriate statistical model for the variable interest. Hence,

i) define the variable, X.

ii) write the complete probability density function

iii) find its mean and variance. all in their commonly used forms and symbols.

Answer 1

i) As we are given here that the amount of time a technician needs to fix a wheel bearing problem is between 1.5 and 4.0 hours, therefore the distribution for the random variable X that would be most appropriate would be given as:

ii) The PDF for X here is given as:

This is the required PDF for X here.

iiii) The mean and variance here are computed as:

Mean = (a + b) / 2 = (1.5 + 4) / 2 = 2.75

Therefore 2.75 is the required mean here.

The variance here is computed as:

Variance = (b - a)² / 12 = (4 - 1.5)² / 12 = 0.5208

Therefore 0.5208 is the required variance here.