document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207223>Question 1207223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3. The Edwards's Theater chain has studied its morie customers to determine how much money they spend on concessions. The study revealed that the spending distribution is approximately normally distributed with a man of 84.11 and a standard deviation of 81.37.\r<BR>\n" );
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document.write( "a) What percentage of customers will spend less than $2.50 on concessions\"\r<BR>\n" );
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document.write( "(b) What percentage of the customers will spend between 83.00 to $4.20 cm concession?\r<BR>\n" );
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document.write( "(c) You got free tea if you spend more than 86.00. How many people are likely to get tea if 100 people attended the movie. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844979 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the calculator at <a hreef = \"\" target = \"_blank\"></a> can help you find the answer to these questions.\r<BR>\n" );
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document.write( "here are the results.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/050701.jpg\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/050702.jpg\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/050703.jpg\">\r<BR>\n" );
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document.write( "this calculator can work directly off the raw scores or off the z-scores.\r<BR>\n" );
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document.write( "to show you how it works off the z-scores, we'll take the second problem that calculates the probability of between 4.2 and 83.\r<BR>\n" );
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document.write( "to work off z-scores, you set the mean to 0 and the standard deviation to 1.\r<BR>\n" );
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document.write( "you find the z-score for 4.2 and the z-score for 83.\r<BR>\n" );
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document.write( "z = (x-m)/s is the z-score formula.<BR>\n" );
document.write( "z is the z-score.<BR>\n" );
document.write( "x is the raw score.<BR>\n" );
document.write( "m is the raw mean.<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "for raw score of 4.2, formula becomes z = (4.2 - 84.11) / 81.37 = -.982057 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "for raw score of 83, formula becomes z = (83 - 84.11) / 81.37 = -.013641 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "set the calculator mean to 0 and the calculator standard deviation to 1 and find the probability of getting a z-score between -.982057 and -.013641.\r<BR>\n" );
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document.write( "the results are shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/050706.jpg\">\r<BR>\n" );
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document.write( "the calculator tells you that the probability is .3325.<BR>\n" );
document.write( "this is the same as the probability we got earlier when working directly with raw scores.<BR>\n" );
document.write( "prior to the user of calculators, you has to get the z-score first and then work off the z-score.<BR>\n" );
document.write( "the calculators do that work for you, but it's still useful to know how to work with the z-scores,\r<BR>\n" );
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document.write( " </SPAN>\n" );
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