document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192927>Question 1192927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood). The distribution of X for a healthy person is normally distributed with men μ = 85 and standard deviation σ = 25. A person suffers from severe excess in insulin would have a lower level of glucose. A blood test with result of X < 40 would be used as an indicator that medication is needed.<BR>\n" );
document.write( "(a) What is the probability that a healthy person will be suggested with medication after a single test?<BR>\n" );
document.write( "̅<BR>\n" );
document.write( "(b) A doctor uses the average result of 2 tests for diagnosis, that is 𝑋. The second test will be conducted<BR>\n" );
document.write( "one week after the first test, so that the two test results are independent. For many healthy persons, each<BR>\n" );
document.write( "̅ has finished two tests, find the expectation and standard error of the distribution of 𝑋.<BR>\n" );
document.write( "(c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests<BR>\n" );
document.write( "̅<BR>\n" );
document.write( "is less than 40, that is 𝑋 < 40, so to reduce the chance of unnecessary use of medication on a healthy<BR>\n" );
document.write( "person. Use the distribution in part (b)) to find the probability that a healthy person will be suggested with medication after 2 tests to verify this doctor’s theory.<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 #824879 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. z=(x-mean)/sd so z< (40-85)/25=-45/25 or -1.8<BR>\n" );
document.write( "That probability is 0.0359<BR>\n" );
document.write( "b. for two tests the expectation of the mean is still 85 mg%<BR>\n" );
document.write( "The SE is the sd/sqrt(n) or 25/sqrt(2)=17.68<BR>\n" );
document.write( "now z would b <-40/17.68=-2.26<BR>\n" );
document.write( "That probability is 0.0119 </SPAN>\n" );
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