document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=535147>Question 535147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It was found out that average intake of medicine in a group of patients is 110mg with standard deviation 10mg per week.<BR>\n" );
document.write( "(a) a patient is chosen at random. Find the probability that his/her intake is in betweem 100mg and 115mg per week.<BR>\n" );
document.write( "(b) a sample of 3 patients is chosen at random. Find the probability that the sample mean (average) intake exceeds 115mg per week. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351783 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=351783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It was found out that average intake of medicine in a group of patients is 110mg with standard deviation 10mg per week.<BR>\n" );
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document.write( "(a) a patient is chosen at random. Find the probability that his/her intake is in betweem 100mg and 115mg per week.<BR>\n" );
document.write( "z(100) = (100-110)/10 = -1 <BR>\n" );
document.write( "z(115) = (115-110)/10 = 1/2<BR>\n" );
document.write( "P(100 < x < 115) = P(-1< z <1/2) = 0.5328<BR>\n" );
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document.write( "(b) a sample of 3 patients is chosen at random. Find the probability that the sample mean (average) intake exceeds 115mg per week.<BR>\n" );
document.write( "t(115) = (115-110)/(10/sqrt(3)) = 5/(10/sqrt(3)) = 0.8660<BR>\n" );
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document.write( "P(x > 115) = P(t > 0.8660 when df = 2) = 0.2388<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );