document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160975>Question 1160975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John surfs the website on a regular basis. Suppose the time he spent surfing the website per day is normally distributed, µ = 8 minutes and σ = 2 minutes. If you select a random sample of 4 sessions, <BR>\n" );
document.write( "a.	What is the probability that the sample mean is less than 8 minutes?<BR>\n" );
document.write( "b.	What is the probability that sample mean is between 8 and 10 minutes?<BR>\n" );
document.write( "c.	If you select a random sample of 16 sessions, what is the probability that a as sample mean is between 8 and 9 minutes?<BR>\n" );
document.write( "d.	Explain the differences in the results of (b) and (c).<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 #784622 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=784622\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. 50%, since E(X bar)=8 minutes\r<BR>\n" );
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document.write( "z=(x bar-mean)/sigma/sqrt(n)<BR>\n" );
document.write( "sigma/sqrt(n)=2/2=1<BR>\n" );
document.write( "so b is looking at 8 and 10 minutes with sd 1<BR>\n" );
document.write( "this is z between 0 and 2, which is 0.4772.\r<BR>\n" );
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document.write( "for 16 now the sd will be 2/sqrt(16)=0.5<BR>\n" );
document.write( "and the same probability of 0.4772 will occur. \r<BR>\n" );
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document.write( "It is much more likely that the sampling distribution will be narrower and distances from the expected value of 8 (in this instance) won't be as much as the sample size increases.   </SPAN>\n" );
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