document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018287>Question 1018287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches? </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "the diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "This is a problem solved using the normal distribution, or the equivalent on the calculator.<BR>\n" );
document.write( " <BR>\n" );
document.write( "First we need to find the Z-score, where<BR>\n" );
document.write( "Z=(X-&mu;)/&sigma;<BR>\n" );
document.write( "=(0.293-0.30)/0.01<BR>\n" );
document.write( "=-0.7<BR>\n" );
document.write( "where<BR>\n" );
document.write( "X=0.293 (the desired upper limit)<BR>\n" );
document.write( "&mu;=mean,<BR>\n" );
document.write( "&sigma;=standard deviation.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Next we look up the normal distribution for Z=-0.7 and find the probability of Z<=-0.07 as 0.24196. Which means<BR>\n" );
document.write( "P(X<=0.293)=0.24196<BR>\n" );
document.write( "for 460 pencils, we expect 460*0.24196=111.3\r<BR>\n" );
document.write( "\n" );
document.write( "So the diameter of 111 pencils are expected to be less than or equal to be 0.293 inches or less.<BR>\n" );
document.write( " </SPAN>\n" );
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