Question

Problem 1 [4 pts]: The maintenance cost of machines are uniformly distributed from 0 to 160 (dollars). If a random sample of 75 machines is taken from a factory, (a). find the mean aggregate (total) maintenance cost for a sample of 75 machines.

Answer 1

$6,000

Explanation:

The mean value of a sample is assumed to be the same as the mean of the population. The mean of a uniformly distributed variable between 0 and 160 is:

`M = (0+160)/(2)\\ M=\$80`

If the mean cost for each machine is $80, the mean aggregate cost for a sample of 75 machines is:

`M_(75)=75*\$80\\M_(75)=\$6,000`

The mean aggregate maintenance cost is $6,000.