The probability density function for the life span of an electronics part is where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places.
A)0.487
B)0.513
C)0.532
D)0.497
E)0.468

Question

The probability density function for the life span of an electronics part is  where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places. ​
A)0.487 
B)0.513 
C)0.532 
D)0.497 
E)0.468

Quizplus · Accepted Answer

To find the probability that a given part lasts longer than 18 months, we need to integrate the given probability density function from 18 to infinity.

P(X > 18) = ∫[18, ∞) 11e^(-0.03t) dt

Using integration by parts and simplifying, we get:

P(X > 18) = e^(-0.03*18) = e^(-0.54) ≈ 0.487

Therefore, the answer is choice A) 0.487.

The Probability Density Function for the Life Span of an Electronics