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 four hours. (a) Find the probability that a randomly selected furnace repair requires more than two hours. (b) Find the probability that a randomly selected furnace repair requires less than two hours.

Answer 1

Let X : Amount of time a repairman needs to fix a furnace

Amount of time a repairman needs to fix a furnace is uniformly distributed between 1.5 and four hours.

X ~ U(1.5 , 4)

f(X) = $\frac{1}{2.5}$

We know that CDF of Uniform distribution is given by

If X~ U(a,b) then P(X<=x) = $\frac{x-a}{b-a}$

Here X~ U(1.5,4) then P(X<=x) = $\frac{x-1.5}{2.5}$

(a)

probability that randomly selected furnace repair requires more than 2 hours = P(X>2)

$P(X>2) = 1- P(X\le2)$

  $= 1- \frac{2-1.5}{2.5}= 1-0.2 = 0.8$

Probability that randomly selected furnace repair requires more than 2 hours is 0.8

(b)

Probability that randomly selected furnace repair requires less than two hours = P(X<2)

$P(X<2) = \frac{2-1.5}{2.5}=0.2$

Probability that randomly selected furnace repair requires less than two hours is 0.2