Question

In: Statistics and Probability

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims...

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 118 watts with a variance of 121 . What is the probability that the mean amplifier output would differ from the population mean by greater than 0.6 watts in a sample of 77 amplifiers if the claim is true? Round your answer to four decimal places.

Solutions

Expert Solution

Solution :

Given that,

mean = = 118

standard deviation = = 11

n = 77

= = 118

= / n = 11 / 77 = 1.2536

P(117.4 < < 118.6) = P((117 - 118) / 1.2536<( - ) / < (118.6 - 118) / 1.2536))

=1 - (P(-0.48 < Z <0.48))

= 1 - ( P(Z < 0.48) - P(Z < -0.48))

= 1 - (0.6844 - 0.3156)

= 1 - 0.3688

= 0.6312

The probability is 0.6312


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