document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270623>Question 270623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with this question: Determine the approximate probability that a sample average (x-bar) taken from some population with the mean = 50 and standard deviation = 4 exceeds 50.6, where the sample size is 100? </SPAN>\n" );
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document.write( "Determine the approximate probability that a sample average (x-bar) taken from some population with the mean = 50 and standard deviation = 4 exceeds 50.6, where the sample size is 100?\r<BR>\n" );
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document.write( "The Central Limit Theory tells you something about the <BR>\n" );
document.write( "distribution of the means of samples of a given size, n.<BR>\n" );
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document.write( "It says the mean of the sample means is the same as the<BR>\n" );
document.write( "mean of the population.<BR>\n" );
document.write( "It says the standard deviation of the sample means is <BR>\n" );
document.write( "(standard deviation of the population)/(sqrt(sample size).<BR>\n" );
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document.write( "Your Problem:<BR>\n" );
document.write( "The z-score of 50.6 = (50.6-50)/[4/sqrt(100)] = 0.6*10/4 = 1.5<BR>\n" );
document.write( "P(x-bar > 50.6) = P(z > 1.5) = normalcdf(1.5,100) = 0.0668<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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