document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011534>Question 1011534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.\r<BR>\n" );
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document.write( "a. 121.6, 152.4<BR>\n" );
document.write( "b. 121.6, 150.4<BR>\n" );
document.write( "c. 123,6, 150.4<BR>\n" );
document.write( "d. 122.6, 148.4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627321 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 136<BR>\n" );
document.write( "standard deviation is 12.\r<BR>\n" );
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document.write( "your confidence interval is .7698.\r<BR>\n" );
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document.write( "that's a two tailed confidence interval, so your alpha is (1 - .7698) / 2 = .1151.\r<BR>\n" );
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document.write( "that alpha would be on each end of the normal disribution curve.\r<BR>\n" );
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document.write( "you would look up a z-score with an area of .1151 to the left of it.\r<BR>\n" );
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document.write( "that's your low z-score.\r<BR>\n" );
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document.write( "you would look up a z-score with an area of .1151 to the right of it.\r<BR>\n" );
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document.write( "that equates to a z-score with an area of 1 - .1151 = .8849 to the left of it.\r<BR>\n" );
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document.write( "you can look these up in the z-score table, or you can use a calculator.\r<BR>\n" );
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document.write( "if you used the z-score table, you would  find the z-scores to be between -1.2 and 1.2.\r<BR>\n" );
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document.write( "since these were found firectly from the table, the calculator should give you the same result.\r<BR>\n" );
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document.write( "i used my ti-84 plus and got z-score between -1.199843825 and 1.99843825.\r<BR>\n" );
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document.write( "this rounds to between -1.2 and 1.2, so the results are comparable, even though the calculator gets into more detail than the table.\r<BR>\n" );
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document.write( "the table i used can be found here:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\" target = \"_blank\">http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdfhttp://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf</a>\r<BR>\n" );
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document.write( "there is also an online z-score calculator that will find it for you and show you what it looks like graphically.\r<BR>\n" );
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document.write( "that calculator can be found here:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "a picture of the results from your problem is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/122701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "now you want to translate the z-score into a raw-score.\r<BR>\n" );
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document.write( "the formula for that is:\r<BR>\n" );
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document.write( "z = (x-m)/s\r<BR>\n" );
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document.write( "x is the z-score.<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "z1 = -1.2 = the low z-score.<BR>\n" );
document.write( "z2 = 1.2 = the high z-score.<BR>\n" );
document.write( "x1 is the low raw score you want to find.<BR>\n" );
document.write( "x2 is the high raw score you want to find.<BR>\n" );
document.write( "m = 136 is the mean of the systolic blood pressure from all patients measured at the hospital.<BR>\n" );
document.write( "s = 12 is the standard deviation.\r<BR>\n" );
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document.write( "a normal distribution is assumed.\r<BR>\n" );
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document.write( "the formula for the low score is z1 = (x1 - m) / s which is equal to -1.2 = (x1 - 136) / 12.<BR>\n" );
document.write( "solve for x1 to get x1 = 12 * -1.2 + 136 = 121.6.\r<BR>\n" );
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document.write( "the formula for the high score is z2 = (x2 - m) / s which is equal to 1.2 = (x1 - 136) / 12.<BR>\n" );
document.write( "solve for x2 to get x2 = 12 * 1.2 + 136 = 150.4\r<BR>\n" );
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document.write( "you have a low score of 121.6 and a high score of 150.4\r<BR>\n" );
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document.write( "that should be selection b.\r<BR>\n" );
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document.write( "a picture of what that looks like, using the online graphing calculator, is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/122702.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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