Question

The life of a fully-charged cell phone battery is normally distributed with a mean of 14 hours with a standard deviation of 3 hours. What is the probability that 25 batteries last at least 13 hours?

Answer #1

The probability that 25 batteries last at least 13 hours is

P(Xbar > 13) = P(Z > (13 - Mean) / (SD / sqrt(n))

= P(Z > (13 - 14) / (3/sqrt(25))

= P(Z > -1.6667)

= 1 - P(Z < -1.6667)

= 1 - 0.0478 = 0.9522

Therefore, The probability that 25 batteries last at least 13 hours is 0.9522

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