document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=354335>Question 354335</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A supplier contract calls for a key dimension of a part to be between 1.95 and 2.05 cm.  The supplier has determined that the standard deviation of its process which is normally distributed, is 0.10 cm.  \r<BR>\n" );
document.write( "\n" );
document.write( "a. If the mean is 1.98, what fraction of parts will meet specifications?<BR>\n" );
document.write( "b. If the mean is adjusted to 2.00, what fraction of the parts will meet specifications?<BR>\n" );
document.write( "c.  How small must the standard deviation be to ensure that no more than 2% of parts are nonconforming, assuming the mean is 2.oo? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #253226 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=253226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A supplier contract calls for a key dimension of a part to be between 1.95 and 2.05 cm. The supplier has determined that the standard deviation of its process which is normally distributed, is 0.10 cm. <BR>\n" );
document.write( "a. If the mean is 1.98, what fraction of parts will meet specifications?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z(1.95) = (1.95-1.98)/0.1 = -.3000  <BR>\n" );
document.write( "z(2.05) = (2.05-1.98)/0.1 = 0.7<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(1.95< x <1.98) = P(-0.3 < z < 0.7) = normalcdf(-0.3,0.7) = 0.3759<BR>\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "b. If the mean is adjusted to 2.00, what fraction of the parts will meet specifications?<BR>\n" );
document.write( "Same procedure as used in part a.<BR>\n" );
document.write( "----------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "c. How small must the standard deviation be to ensure that no more than 2% of parts are nonconforming, assuming the mean is 2.oo?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z-value with a left-tail of 1% and a right tail of 1%<BR>\n" );
document.write( "invNorm(0.01) = +/-2.3264<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Solve :: <BR>\n" );
document.write( "(1.95-2)/s = -2.3264<BR>\n" );
document.write( "s = 0.0215<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "(2.05-2)/s = 2.3264<BR>\n" );
document.write( "s = 0.0215<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );