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Trainees must complete a specific task in less than 2 minutes.
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:
2 years ago.
Category:
Calculus and Above
Expert:
Sandhya_sharma
replied 2 years ago.
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Expert:
Sandhya_sharma
replied 2 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
Answer: 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
Answer: 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
Answer: 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
Answer: 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
Answer: 0.7733
6)If X represents the time it takes to complete the task, what is Var(X)? Give your answer to four decimal places.
Var(X) = E(X^2) – (E(X))^2
= 0.7733 – 0.72^2
= 0.2549
Answer: 0.2549
Sandhya_sharma, Master's Degree
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Calculus and Above
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I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.
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