Suppose that a random sample of size 64 is to be selected from a population with

Question

Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5 What are the mean and standard deviation of the Sampling distribution?(Round the answer to three decimal places.) mu G = sigma_x = What is the approximate probability that x^- will be within 0.4 of the population mean mu? (Round the answer to four decimal places.) P = What is the approximate probability that x^- will differ from mu by more than 0.8? (Round the answer to four decimal places.) P =

Explanation / Answer

ans=

mean of the x-bar sampling distribution = 40
standard deviation of the x-bar sampling distribution = 5/sqrt(64) = 5/8 = 0.625

b)
P( 39.4 < x-bar < 40.4)

Mean = 40
Standard deviation = 5
Standard error / n = 5 / 64 = 0.625
standardize xbar to z = (xbar - ) / ( / n )
P( 39.8 < xbar < 40.5) = P[( 39.8 - 40) / 0.625 < z < ( 40.4 - 40) / 0.625]
P( -0.64 < z < 0.64) = 0.7389
(from normal probability table)

c)
P( x-bar-mu > 0.8) = P(x-bar > 40.8)
Mean = 40
Standard deviation = 5
Standard error / n = 5 / 64 = 0.625
standardize xbar to z = (xbar - ) / ( / n )
P(xbar > 40.8) = P( z > (40.8-40) / 0.625)
= P(z > 1.28) =0.1003
(from normal probability table)

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