document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189250>Question 189250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A standard test for diabetes is based on glucose levels in the blood after fasting for a prescribed period. For untreated diabetics the mean fasting glucose is found to be 11.74mmol/L, and the standard deviation is 3.50mmol/L. The level of glucose appears to be approximately normally distributed. <BR>\n" );
document.write( "To operate a simple diagnostic test based on fasting glucose levels, we need to set a cut off point, C, so that if the patients fasting glucose level is at least C we say they have diabetes. If it is lower we say they do not have diabetes. \r<BR>\n" );
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document.write( "(i) For the moment, suppose we use C=6.5. What is the probability that a diabetic is incorrectly diagnosed as not having diabetes? \r<BR>\n" );
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document.write( "NOTE: I have attempted this question, but got stuck, because I'm not sure if what I'm doing is correct. I found that the P(6.5 < x < 11.74) = 0.4325, but don't know where to go from here...<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 #141978 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=141978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A standard test for diabetes is based on glucose levels in the blood after fasting for a prescribed period. For untreated diabetics the mean fasting glucose is found to be 11.74mmol/L, and the standard deviation is 3.50mmol/L. The level of glucose appears to be approximately normally distributed. <BR>\n" );
document.write( "To operate a simple diagnostic test based on fasting glucose levels, we need to set a cut off point, C, so that if the patients fasting glucose level is at least C we say they have diabetes. If it is lower we say they do not have diabetes. <BR>\n" );
document.write( "(i) For the moment, suppose we use C=6.5. What is the probability that a diabetic is incorrectly diagnosed as not having diabetes? <BR>\n" );
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document.write( "Those with glucose above 6.5 will be diagnosed \"diabetic\"<BR>\n" );
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document.write( "Those below 6.5 will be diagnosed \"non-diabetic\"<BR>\n" );
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document.write( "Find the z-value of 6.5.<BR>\n" );
document.write( "z(6.5) = (6.5-11.74)/3.5 = -1.4971<BR>\n" );
document.write( "P(a person is diagnosed non-diabetic) = P(z < -1.4971) = 0.0672<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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