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Question 1: An undergraduate business student has purchased a laptop computer for use during exams. This...

Question 1:

An undergraduate business student has purchased a laptop computer for use during exams. This laptop is perfectly reliable except for two parts: its microchip, which has a MTBF=20 hours; and its battery, which has a MTBF=10 hours. Also, on average the battery will wear out in five hours, with a standard deviation of 30 minutes. Assuming that a new battery has just been installed, what is the probability that the laptop will perform reliably during a one-hour exam?

0.85

0.855

0.9

0.95

1.85

Question 2

An undergraduate business student has purchased a laptop computer for use during exams. This laptop is perfectly reliable except for two parts: its microchip, which has a MTBF = 20 hours; and its battery, which has a MTBF = 10 hours. Also, on average the battery will wear out in five hours, with a standard deviation of 30 minutes. Assuming that a new battery has just been installed and the student brings one spare, fully charged battery with him, what is the probability that the laptop will perform reliably during a one-hour exam?

Question 6 options:

0.89775

0.9405

0.987525

0.99

0.9975

Question 3

An undergraduate business student has purchased a laptop computer for use during exams. This laptop is perfectly reliable except for two parts: its microchip, which has a MTBF = 20 hours; and its battery, which has a MTBF = 10 hours. Also, on average the battery will wear out in five hours, with a standard deviation of 30 minutes. What is the probability that a new battery will wear out within six hours?

0.0228

0.4772

0.5

0.9544

0.9772

Question 4:

An undergraduate business student has purchased a laptop computer for use during exams. This laptop is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. Also, on average the battery will wear out in five hours, with a standard deviation of 30 minutes. What maximum battery life should the manufacturer specify in order to have a .1587 probability that a battery will wear out within that amount of time?

3.5 hours

4 hours

4.5 hours

5 hours

5.5 hours
math   Statistics-And-Probability   
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Answer #1

Question 1

For t = 1 hour,

Reliability of microchip = e-1/20 = 0.95

Reliability of battery = e-1/10 = 0.90

z value for 1 hour for battery wearing out = (1-5)/.5 = -8, F(z) = 0

Probability of battery not wearing out in 1 hour = 1 - 0 = 1

Probability that the laptop will perform reliably during a one-hour exam = Reliability of microchip * Reliability of battery * Probability of battery not wearing out in 1 hour

= 0.95*0.90*1

= 0.855

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