Question

Ace Heating and Air Conditioning Service finds that the amount of time a repairman needs to fix a furnace is uniformly distributed between 1.5 and 4 hours. Let x = the time needed to fix a furnace.

Find the problem that a randomly selected furnace repair requires more than 2 hours.

Answer 1

The probability that a furnace repair requires more than two hours, given a uniform distribution between 1.5 and 4 hours, is 80%.

Step-by-step explanation:

The student is struggling to find the probability that a furnace repair takes more than two hours when the repair time is uniformly distributed between 1.5 and 4 hours.

To find the probability of a repair taking more than two hours, we must calculate the area under the uniform distribution curve from 2 hours to the maximum of 4 hours. Since this is a uniform distribution, the probability density function (pdf) is constant. The total area under the distribution between 1.5 and 4 is 1 (since this is a probability distribution). The length of the interval from 1.5 to 4 is 2.5 hours. Therefore, the constant value of pdf is 1/2.5 = 0.4 per hour. The interval from 2 to 4 is 2 hours long. Thus, the probability that the repair time is more than 2 hours is 0.4 * 2 = 0.8 or 80%.