An undergraduate business student has purchased a laptop computer for use during

Question

An undergraduate business student has purchased a laptop computer for use during the upcoming semester. This laptop is very reliable, but she is concerned that the battery will wear out before the end of the semester. According to the Manufacturer, on average the battery will wear out in 100 hours, with a standard deviation of 5 hours. After looking at her course schedule, she anticipates 90 hours of time will be needed working on the laptop. What is the probability that the battery will last this amount of time or longer?

Explanation / Answer

Assuming normal distribution for battery lifetime of laptop,

Mean = 100 hours

Standard deviation = 5 hours

P(X < A) = P(Z < (A - mean)/standard deviation)

P(battery will last longer than 90 hours) = P(X > 90)

= 1 - P(X < 90)

= 1 - P(Z < (90- 100)/5)

= 1 - P(Z < -2)

= 1 - 0.0228 (from stanmdard normal distribution table)

= 0.9772

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