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 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?

Answer 1

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

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