Question

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

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