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 4 months? Round to 3 decimal places.

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 4 months? Round to 3 decimal places. ​

Quizplus · Accepted Answer

To find the probability that a transmission lasts more than 4 months, we need to calculate the integral of the probability density function from 4 to infinity:

P(t > 4) = ∫4∞ 11ea984b_b0bb_112b_9029_3ddbbb952f7d_TB4005_11 dt

We can use the formula for the exponential probability density function:

f(t) = λe^(-λt)

where λ = 11ea984b_b0bb_112b_9029_3ddbbb952f7d_TB4005_11

Substitute λ into the formula:

P(t > 4) = ∫4∞ λe^(-λt) dt

= [-e^(-λt)]4∞

= e^(-λ*4)

= e^(-11ea984b_b0bb_112b_9029_3ddbbb952f7d_TB4005_11*4)

≈ 0.165

Therefore, the best choice is C with a probability of 0.165.

A Transmission Repair Firm That Wants to Offer a Lifetime