document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156965>Question 1156965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Suppose it is known that the distribution of purchase amounts by customers entering a<BR>\n" );
document.write( "popular retail store is approximately normal with mean $75 and standard deviation<BR>\n" );
document.write( "$20.\r<BR>\n" );
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document.write( "a. What is the probability that a randomly selected customer spends less than $85<BR>\n" );
document.write( "at this store?<BR>\n" );
document.write( "b. What is the probability that a randomly selected customer spends between $65<BR>\n" );
document.write( "and $85 at this store?<BR>\n" );
document.write( "c. What is the probability that a randomly selected customer spends more than<BR>\n" );
document.write( "$45 at this store?<BR>\n" );
document.write( "d. Find the dollar amount such that 80% of all customers spend at least this<BR>\n" );
document.write( "amount.<BR>\n" );
document.write( "e. Find two dollar amounts, equidistant from the mean, such that 90% of all<BR>\n" );
document.write( "customer purchases are between these values. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780121 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780121\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "a. this is (85-75)/20=z and want z<0.5.  prob is 0.6915<BR>\n" );
document.write( "b. This is a z between -0.5 and +0.5. probability is 0.3829<BR>\n" );
document.write( "c. this is a z> -1.5 with probability 0.9332<BR>\n" );
document.write( "d.80% is the area between z=-1.282 and +1.282 <BR>\n" );
document.write( "1.282=(x-mean)sd and -1.282=(x-mean)/sd<BR>\n" );
document.write( "25.64=x-mean or $100.64 top end <BR>\n" );
document.write( "and $49.36 bottom end.   ($49.36, $100.64)\r<BR>\n" );
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document.write( "1.645 =(x-mean)/sd<BR>\n" );
document.write( "32.90=x-mean and -32.90=(x-mean)<BR>\n" );
document.write( "($42.10, $107.90) </SPAN>\n" );
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