Question 1111199
The population mean is 500 and the population standard deviation is 100
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(a)  the sample size is 64
standard deviation of the sample mean is population standard deviation / the square root of the sample size
:
standard deviation of the sample mean = 100/square root(64) = 100/8 = 12.5
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(b)  let X be the sample mean variable
Probability (P) ( 475 < X < 525 ) = P ( X < 525 ) - P ( X < 475 )
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calculate z-scores for each probability
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z-score (525) = (525 - 500) / 12.5 = 2
z-score (475) = (475 - 500) / 12.5 = -2
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lookup the P for each of the z-scores in the table of z-values
:
Probability (P) ( 475 < X < 525 ) = 0.9772 - 0.0228 = 0.9544
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