document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204474>Question 1204474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The mean pulse rate for adults is 72 beats per minute (www.healthepic.com) and let’s suppose that the standard deviation is 9 bpm.  Find:<BR>\n" );
document.write( "a.  	The probability that a randomly chosen adult has a pulse rate over 77 bpm assuming that the rates are normally distributed.<BR>\n" );
document.write( "b.	The probability that a random sample of 18 adults will have a mean beats per minute over 77\r<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 #840761 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=840761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 72 beats per minute.<BR>\n" );
document.write( "standard deviation is 9 beats per minute (supposed).\r<BR>\n" );
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document.write( "probabiiity that a random person has over 77 beats per minue = .2893.\r<BR>\n" );
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document.write( "probbility that the mean of a random sample has over 77 beats per minute = .0092.\r<BR>\n" );
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document.write( "here are the resuts, using the calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "the differnce is that, for an individual sample, the standard deviation is used, while for the mean of a random sample, the standard error is used.\r<BR>\n" );
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document.write( "standard error = standard deviation / square root of sample size = 9 / sqrt(18) = 2.1213.\r<BR>\n" );
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document.write( "the standard error is defined as the standard deviation of the distribution of sample means.<BR>\n" );
document.write( "this is different than the distribution of individual samples.<BR>\n" );
document.write( "as the size of the sample gets larger, the standard error gets smaller.\r<BR>\n" );
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