document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152431>Question 1152431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose certain coins have weights that are normally distributed with a mean of 5.078 g and a standard deviation of 0.072 g. A vending machine is configured to accept those coins with weights between 4.948 g and 5.208 g.<BR>\n" );
document.write( "a. If 270 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins?<BR>\n" );
document.write( "The expected number of rejected coins is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774603 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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/cgi-bin/show-face.mpl?user=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=774603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Probability coin is less than 4.948 grams:<BR>\n" );
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document.write( "z-score = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284.948+-+5.078%29%2F0.072 ALIGN=MIDDLE  ALT=\"%284.948+-+5.078%29%2F0.072\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-0.130%29%2F0.072 ALIGN=MIDDLE  ALT=\"%28-0.130%29%2F0.072\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.81<BR>\n" );
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document.write( "Look up -1.81 on a z-table.  You get an answer of 0.0351. This is the probability the a coin is less than 4.948 grams.<BR>\n" );
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document.write( "Probability coin is more than 5.208 grams:<BR>\n" );
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document.write( "z-score = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285.208+-+5.078%29%2F0.072 ALIGN=MIDDLE  ALT=\"%285.208+-+5.078%29%2F0.072\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.130%2F0.072 ALIGN=MIDDLE  ALT=\"0.130%2F0.072\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.81<BR>\n" );
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document.write( "Look up 1.81 on a z-table.  You get an answer of 0.9649.  This is the probability a coin is LESS than 5.208 grams.  We want to find the probability a coin is MORE than 5.208 grams.  So, if the probability a coin is less than 5.208 grams is 0.9649, the probability it is more than 5.208 grams is 0.0351.  <BR>\n" );
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document.write( "So, the probability the coin does NOT fall in the accepted range is 0.0351 + 0.0351...or 0.0702.<BR>\n" );
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document.write( "Because there are 270 coins, and the probability a coin will be rejected is 0.0702, the number of expected rejected coins is:<BR>\n" );
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document.write( "270 * 0.0702 = 18.954...or, rounded off, 19. </SPAN>\n" );
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