A transmission repair firm that wants to offer a lifetime warranty on its repairs has determined that the probability density function for transmission failure after repair is , where t is the number of months after repair. What is the probability that a transmission chosen at random will last more than 2 months? Round to 3 decimal places.
A)0.348
B)0.248
C)0.497
D)0.546
E)0.447

Question

A transmission repair firm that wants to offer a lifetime warranty on its repairs has determined that the probability density function for transmission failure after repair is  , where t is the number of months after repair. What is the probability that a transmission chosen at random will last more than 2 months? Round to 3 decimal places. ​
A)0.348 
B)0.248 
C)0.497 
D)0.546 
E)0.447

Quizplus · Accepted Answer

To find the probability that a transmission chosen at random will last more than 2 months, we need to solve for:
P(t>2) = ∫2to∞11eb0d3b_98a9_5e44_9790_9bfdffaca4a1_TB1243_11 dt
This integral can be solved using integration by substitution. After finding the antiderivative and evaluating the integral from 2 to infinity, we get:
P(t>2) = e^(−11∙e^(−2)) = 0.497 (rounded to 3 decimal places)
Therefore, the best choice is C.

A Transmission Repair Firm That Wants to Offer a Lifetime