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# - Quiz 1 Review Questions and Solutions Question 1 John Doe has an Applied Probability quiz on Saturday morning His is worried whether he will be

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Quiz 1 Review Questions and Solutions Question 1 John Doe has an Applied Probability quiz on Saturday morning. His is worried whether he will be able to do his last minute studying and still get enough rest. He is confident that if he gets to bed by 1:00 AM, he’ll feel rested enough to take the quiz. Based on all his previous exams, he knows that the amount of studying time he will need is normally distributed with mean = 3.5 hours and standard deviation =1.2 hours. If it is currently 9:00 PM (John is a good student and went to the review session), what is the probability that he will make it to bed in time to feel rested enough in the morning? Let Y denote the time it takes John to finish his studying. P(Go to bed in time) = P(Y < 4) =P(Z < (4 - 3.5)/1.2) = P(Z < 0.42) = 0.6628. Question 2 A particular system in a space vehicle must work properly in order for the space vehicle to re-enter the Earth’s atmosphere. One particular component of the system operates successfully only 85% of the time. To increase the reliability of the system, four identical versions of the components will be installed in such a way that the system will operate successfully if at least one component is working successfully. Assume the four components operate independently. What is the probability that the system will fail? Let ( p i ) be the probability that component i of the system operates successfully and( pi’) be the probability that component i of the system fails. Therefore, p i = .85 and ( p i ’) =.15 for i =1, 2, 3, 4. If at least one component is operational, then the system will remain operational. Therefore, the only way in which the system fails is if ALL components fail. Because the

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## This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.

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- Quiz 1 Review Questions and Solutions Question 1 John Doe has an Applied Probability quiz on Saturday morning His is worried whether he will be

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