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 |
Solution:-
Given that,
mean = = 5 hours
standard deviation = = 30 minutes = 0.5 hours
Using standard normal table,
P(Z > z) = 0.1587
= 1 - P(Z < z) = 0.1587
= P(Z < z) = 1 - 0.1587
= P(Z < z ) = 0.8413
= P(Z < 1.00 ) = 0.8413
z = 1.00
Using z-score formula,
x = z * +
x = 1.00 * 0.5 + 5
x = 5.5 hours
Get Answers For Free
Most questions answered within 1 hours.