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 part lasts longer than 18 months we need to integrate the probability density function from 18 to infinity:

P(X > 18) = ∫[18,∞] 11ea984b_b10b_c8e2_9029_9964ad27ba2d_TB4005_11 dt

Using the formula for the gamma function, we can simplify the integral as follows:

P(X > 18) = 1 - Γ(4,11/2) / Γ(4)

Using a calculator or a table of the incomplete gamma function, we find:

P(X > 18) ≈ 0.487

Therefore, the best choice is A.

The Probability Density Function for the Life Span of an Electronics