Given a normal population with standard deviation equal to 4

Given a normal population with standard deviation equal to 4, a random sample of 25 observations is taken. (a) ( 10 points) What is the probability that the sample mean exceeds the population mean by more than 2? What is the probability that the sample mean is more than 3 below the population mean? (c) (10 points) What is the probability that the sample mean differs from the population mean by more than 1?

Solution

6) P(x bar-mu>2) = P(Z>2/(4/5) ) =

P(Z>2.5)

= 0.5-0.4938

= 0.062

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7) P(x bar-mu>3)

= P(Z>3.75) = 0

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c) P(xbar-mu>1) = P(Z>1.25)

= 0.5-0.3944

= 0.1056