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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
reenter 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.
 Spring '07
 JosephGeunes

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