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 |
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
An undergraduate business student has purchased a laptop computer for use during exams. This laptop is...
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?...
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 = 10 hours and its battery, which has a MTBF = 20 hours. Assuming that a new battery has just been installed, what is the probability that the LAPTOP will FAIL during a 2 hour exam?
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