document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037574>Question 1037574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose certain coins have weights that are normally distributed with a mean of 5.368 g and a standard deviation of 0.057 g. A vending machine is configured to accept those coins with weights between 5.258 g and 5.478 g. \r<BR>\n" );
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document.write( "A. If 270 different coins are inserted in the vending machine, what is the expected number of rejected coins? \r<BR>\n" );
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document.write( "B. If 270 different coins are inserted in the vending machine, what is the probability that the mean falls between the limits of 5.258 g and 5.478. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652239 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose certain coins have weights that are normally distributed with a mean of 5.368 g and a standard deviation of 0.057 g. A vending machine is configured to accept those coins with weights between 5.258 g and 5.478 g.<BR>\n" );
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document.write( "z(5.258) = (5.258-5.368)/0.057 = -1.93<BR>\n" );
document.write( "z(5.478) = (5.478-5.368)/0.057 = +1.93<BR>\n" );
document.write( "P(5.258 < x < 5.478) = P(-1.93< z < 1.93) = 0.9464<BR>\n" );
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document.write( "A. If 270 different coins are inserted in the vending machine, what is the expected number of rejected coins?<BR>\n" );
document.write( "Ans: 0.9464*270 = 256 when rounded up<BR>\n" );
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document.write( "B. If 270 different coins are inserted in the vending machine, what is the probability that the mean falls between the limits of 5.258 g and 5.478.<BR>\n" );
document.write( "Comment:: Same procedure but the standard deviation is 0.057/sqrt(270) = 0.0035<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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