document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121626>Question 1121626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the questions below assume that females have pulse rates that are normally distributed with a mean of 74 beats per minute and a standard deviation of 12.5 beats per minute.<BR>\n" );
document.write( "a. If 1 adult female is randomly selected, find the probability that her pulse is greater than 70 beats per minute.<BR>\n" );
document.write( "b. If 25 adult female are randomly selected, find the probability that they have pulse rates with a mean greater than 70 beats per minute.<BR>\n" );
document.write( "c. Why can the normal distribution be used in part (b) above, even though the sample size does not exceed 30?<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 #737580 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=737580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "for a, z>(70-74)/12.5 or z>-0.32.  That probability is 0.6255\r<BR>\n" );
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document.write( "b.  z=(x-mean)/s/sqrt(n) or z>-4*sqrt(25)/12.5 or -1.6  That probability is 0.9452\r<BR>\n" );
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document.write( "c.  If we can assume the population is normally distributed, then any sample size is appropriate.  Thirty is not magic.  If the population is significantly skewed, one may need a lot more than 30 or even a nonparametric test.  If the population is normally distributed, 10 would be fine. </SPAN>\n" );
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