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Category: Calculus and Above
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# Trainees Must Complete A Specific Task In Less Than

### Resolved Question:

Trainees must complete a specific task in less than 2 minutes. Consider the probability density function below for the time it takes a trainee to complete the task.

f(x) = 0.92 - 0.42x 0 < x < 2

1) What is the probability a trainee will complete the task in less than 1.34 minutes? Give your answer to four decimal places.
2)What is the probability that a trainee will complete the task in more than 1.34 minutes? Give your answer to four decimal places.
3)What is the probability it will take a trainee between 0.58 minutes and 1.34 minutes to complete the task? Give your answer to four decimal places.
4)What is the expected time it will take a trainee to complete the task? Give your answer to four decimal places.
5)If X represents the time it takes to complete the task, what is E(X^2) ? Give your answer to four decimal places.
6)If X represents the time it takes to complete the task, what is Var(X)? Give your answer to four decimal places.

Submitted: 5 years ago.
Category: Calculus and Above
Expert:  Sandhya_sharma replied 5 years ago.

1) What is the probability a trainee will complete the task in less than 1.34 minutes? Give your answer to four decimal places.
∫(limit from 0 to 1.34) (0.92 - 0.42x) dx
= [0.92x - 0.21x^2] (limit from 0 to 1.34)
= 0.8557

2) What is the probability that a trainee will complete the task in more than 1.34 minutes? Give your answer to four decimal places.
Probability that a trainee will complete the task in more than 1.34 minutes = 1 – 0.8557 = 0.1443

3)What is the probability it will take a trainee between 0.58 minutes and 1.34 minutes to complete the task? Give your answer to four decimal places.
∫(limit from 0.58 to 1.34) (0.92 - 0.42x) dx
= [0.92x - 0.21x^2] (limit from 0.58 to 1.34)
=0.3928

4)What is the expected time it will take a trainee to complete the task? Give your answer to four decimal places.
∫(limit from 0 to 2) x(0.92 - 0.42x) dx
= [0.46x^2 – 0.14x^3] (limit from 0 to 2)
= 0.7200

5)If X represents the time it takes to complete the task, what is E(X^2) ? Give your answer to four decimal places.
∫(limit from 0 to 2) x^2(0.92 - 0.42x) dx
= [0.92x^3/3 – 0.21x^4/2] (limit from 0 to 2)
= 0.7733