Question

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?

	0.89775
	0.9405
	0.987525
	0.99
	0.9975

Answer 1

For t = 1 hour,

Reliability of microchip = e^-1/20 = 0.95

Reliability of battery = e^-1/10 = 0.90

Reliability of 2 batteries in parallel = (1-(1-.9)^2 = 0.99

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 2 batteries in parallel * Probability of battery not wearing out in 1 hour

= 0.95*0.99*1

= 0.9405