document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=648023>Question 648023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8. The mean of a normal probability distribution is 60; the standard deviation is 5. <BR>\n" );
document.write( "a. About what percent of the observations lie between 55 and 65? <BR>\n" );
document.write( "b. About what percent of the observations lie between 50 and 70? <BR>\n" );
document.write( "c. About what percent of the observations lie between 45 and 75? \r<BR>\n" );
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document.write( "PLEASE HELP!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406530 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=406530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 60.<BR>\n" );
document.write( "standard deviation is 5.<BR>\n" );
document.write( "calculate a z-score for each of the possibilities.<BR>\n" );
document.write( "z-score = actual score minus mean divided by standard deviation.<BR>\n" );
document.write( "for a:<BR>\n" );
document.write( "z-score = (55-60)/5 and (65-60)/5 which results in:<BR>\n" );
document.write( "z-score of -1 and 1.<BR>\n" );
document.write( "this is 1 standard deviation above and below the mean which is approximately 68% of the distribution.<BR>\n" );
document.write( "for b:<BR>\n" );
document.write( "z-score = (50-60)/5 and (70-60)/5 which results in:<BR>\n" );
document.write( "z-score of -2 and 2.<BR>\n" );
document.write( "this is 2 standard deviations above and belowthe mean which is approximately 95% of the distribution.<BR>\n" );
document.write( "for c:<BR>\n" );
document.write( "z-score = (45-60)/5 and (75-60)/5 which results in:<BR>\n" );
document.write( "z-score of -3 and 3.<BR>\n" );
document.write( "this is 3 standard deviations above and below the mean which is approximately 99.7% of the distribution.<BR>\n" );
document.write( "the actual figures are more detailed, but these are the generally recognized rounded figures that are normally used.<BR>\n" );
document.write( "check out this link for further information regarding normal distribution and standard deviations from the mean.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.mathsisfun.com/data/standard-normal-distribution.html\" target = \"_blank\">http://www.mathsisfun.com/data/standard-normal-distribution.html</a> </SPAN>\n" );
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