National Welding uses industrial robots in some of its assembly-line operations. Management has determined that, on average, a robot breaks down after 1,000 hours of use and that the lengths of time between breakdowns are exponentially distributed.
A. What is the probability that a robot selected at random will break down between 300 and 800 hours of use?
Round your answer to two decimal places.
B. What is the probability that a robot will break down after 1,200 hours of use?
Round your answer to two decimal places.
A) a. 0.29, b. 0.3
B) a. 0.61, b. 0.13
C) a. 0.76, b. 0.44
D) a. 0.26, b. 0.61

Question

National Welding uses industrial robots in some of its assembly-line operations. Management has determined that, on average, a robot breaks down after 1,000 hours of use and that the lengths of time between breakdowns are exponentially distributed. 
A. What is the probability that a robot selected at random will break down between 300 and 800 hours of use?
Round your answer to two decimal places.
B. What is the probability that a robot will break down after 1,200 hours of use?
Round your answer to two decimal places.
A) a. 0.29, b. 0.3
B) a. 0.61, b. 0.13
C) a. 0.76, b. 0.44
D) a. 0.26, b. 0.61

Quizplus · Accepted Answer

A. Using the exponential distribution, we can calculate the probability of a breakdown between 300 and 800 hours as follows:
P(300 < X < 800) = e^(-300/1000) - e^(-800/1000) = 0.29
B. The probability of a robot breaking down after 1,200 hours is simply the probability that it lasts longer than 1,200 hours, which is:
P(X > 1200) = e^(-1200/1000) = 0.3

National Welding Uses Industrial Robots in Some of Its Assembly-Line