document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074584>Question 1074584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having troubles with this question:\r<BR>\n" );
document.write( "\n" );
document.write( "Bob’s weekly expenditures at Dining Hall are normally distributed with a mean of $80 and a standard deviation of $10. Bob wants to budget an amount each week he can spend at the cafeteria. How much should Bob budget if he wants to spend less than the budgeted amount 90 percent of the time?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689237 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=689237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Bob’s weekly expenditures at Dining Hall are normally distributed with a mean of $80 and a standard deviation of $10. Bob wants to budget an amount each week he can spend at the cafeteria. How much should Bob budget if he wants to spend less than the budgeted amount 90 percent of the time? \r<BR>\n" );
document.write( "\n" );
document.write( "mean = 80<BR>\n" );
document.write( "standard deviation = 10<BR>\n" );
document.write( "he wants to spend less than the budgeted amount 90 percent of the time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we are looking for the 90th percentile under the normal distribution curve where mean = 80 and standard deviation = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use normal distribution tables to find the area to the left of a particular z-score equal to .9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you will find that the z-score closest to .9 will be the z-score for .8997 and that is z = 1.28.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you use a calculator to find the z-score, you will find that the z-score is more accurately defined as 1.281551567 (through use of TI-84 plus calculator).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "with a mean of 80 and a standard deviation of 10, the z-score will translate to a raw score through the use of the following formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = (x-m)/s\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean of the raw score<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "with 2 decimal accuracy in the elements of the equation, it becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1.28 = (x - 80)/10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = 10 * 1.28 + 80 = 92.8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if he budgets $92.80 each week, then his actual expenditures will be less than his budget 90% of the time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can see this graphically as shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032801.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from this graph, you can see that 90% of the scores will be less than or equal to 92.817 which can be rounded to $92.80.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the graph is showing the distribution of actual expenditures, than a budget of $92.80 will ensure that the actual expenditure will be less than the budget amount 90% of the time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );