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The mean output of a certain type of amplifier is 496 watts with a variance of...

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Basic Math

The mean output of a certain type of amplifier is 496 watts witha variance of 144. If 40 amplifiers are sampled, what is theprobability that the mean of the sample would differ from thepopulation mean by less than 1.2 watts? Round your answer to fourdecimal places.

Answer & Explanation Solved by verified expert
4.1 Ratings (548 Votes)

µ = 496

sd = sqrt(144) = 12

n = 40

sd of sample mean = 12 / sqrt(40) = 1.8974

P(mean of the sample would differ from the population mean by less than 1.2 watts) = P(-1.2/1.8974 < Z < 1.2/1.8974)

                                    = P(-0.63 < Z < 0.63)

                                    = P(Z < 0.63) - P(Z < -0.63)

                                    = 0.7357 - 0.2643

                                    = 0.4714
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