document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1063396>Question 1063396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7d A grinding machine produces components with a mean diameter of 30 mm. All the components are measured and the actual size logged. The standard deviation over a period of time is 0.05 mm. Assuming the normal distribution represents the actual distribution, what is the probability of a component being between 29.95 mm and 30.05 mm diameter?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #678550 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=678550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We use the normal distribution z-tables and the associated probability(P) to solve this problem<BR>\n" );
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document.write( "P ( 29.95 < X < 30.05 ) = P ( X < 30.05 ) - P ( X < 29.95)<BR>\n" );
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document.write( "z-value for 30.05 is (30.05 - 30.00) / 0.05 = 1, therefore<BR>\n" );
document.write( "P ( X < 30.05 ) = 0.8413<BR>\n" );
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document.write( "z-value for 29.95 is (29.95 - 30.00) / 0.05 = -1, therefore<BR>\n" );
document.write( "P ( X < 29.95 ) = 0.1587<BR>\n" );
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document.write( "P ( 29.95 < X < 30.05 ) = 0.8413 - 0.1587 = 0.6826<BR>\n" );
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