document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1038752>Question 1038752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <<>>A set of wrist watch prices are normally distributed with a mean of 76 dollars and a standard deviation of 10 dollars. What proportion of wrist watch prices are between 63 dollars and 90 dollars?<<>>\r<BR>\n" );
document.write( "\n" );
document.write( "I believe this is a z-score problem, so I'd be using the equation (X-mean)/standard deviation<BR>\n" );
document.write( "... I was thinking since it asks for the por potion between 63 and 90 to take the sum & divide by 2.....<BR>\n" );
document.write( " [76-((63+90)/2)]/10 \r<BR>\n" );
document.write( "\n" );
document.write( "Thank you for your help!! <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653470 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=653470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You'll need to calculate two z scores.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For the raw score of x = 63, the z score is...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (x - 76)/10<BR>\n" );
document.write( "z = (63 - 76)/10<BR>\n" );
document.write( "z = -13/10<BR>\n" );
document.write( "z = -1.30\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For the raw score of x = 90, the z score is...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (x - 76)/10<BR>\n" );
document.write( "z = (90 - 76)/10<BR>\n" );
document.write( "z = 14/10<BR>\n" );
document.write( "z = 1.4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we need to find the area under the standard normal bell curve (Z distribution curve) between z = -1.3 and z = 1.4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First find the area to the left of z = -1.3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use this <a  rel=nofollow HREF= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\">table</a> locate the row that starts with \"-1.3\" (page 1) and the column that has 0.00 at the top. The row and column intersect at the value 0.0968\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So this means P(Z < -1.3) = 0.0968<BR>\n" );
document.write( "Basically, the area to the left of z = -1.3 is 0.0968. Let's make M = 0.0968. We'll use this value of M later.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now use the table again to find that<BR>\n" );
document.write( "P(Z < 1.4) = 0.9192<BR>\n" );
document.write( "this value of 0.9192 is found by looking at the row that starts with 1.4 (page 2) and has 0.00 at the top of the column.<BR>\n" );
document.write( "Let's make N = 0.9192\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now subtract the values of N and M (big minus small)<BR>\n" );
document.write( "N - M = 0.9192 - 0.0968 = 0.8224\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the area under the curve between z = -1.3 and z = 1.4 is <font color=red size=5>0.8224</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means the proportion of those between 63 dollars and 90 dollars is <font color=red size=5>0.8224</font> (which is equivalent to roughly 82.24%). This proportion is approximate because the table values are approximate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );