document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092103>Question 1092103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A normal population has a mean of 60 and a standard deviation of 3. You select a sample of 36.<BR>\n" );
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document.write( "Compute the probability the sample mean is (Round z values to 2 decimal places and final answers to 4 decimal places):<BR>\n" );
document.write( "a.	Less than 59.<BR>\n" );
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document.write( "  Probability _____?<BR>\n" );
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document.write( "b.	Between 59 and 61.<BR>\n" );
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document.write( "  Probability _____?<BR>\n" );
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document.write( "c.	Between 61 and 62.<BR>\n" );
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document.write( "  Probability _____?<BR>\n" );
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document.write( "d.	Greater than 62.<BR>\n" );
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document.write( "  Probability _____?<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 #706627 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=706627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> These all make use of finding the z value for each number x where z=(x-mean)/std dev.<BR>\n" );
document.write( "The standard deviation of a sample mean is called the standard error of the mean, and it is sigma/sqrt(n), here 3/6 or 0.5. All the z s are integers, so I didn't write for example -2.00<BR>\n" );
document.write( "for mean < 59 it is (59-60)/0.5=-2 so it is z < -2 or 0.0228<BR>\n" );
document.write( "for mean between 59 and 61 it is z between -2 and +2 or a probability of 0.9545. 59 is 2 sd s to the left of the mean and 61 2 sd s to the right of the mean.<BR>\n" );
document.write( "for mean between 61 and 62 it is 2 < z < 3 or 0.0214<BR>\n" );
document.write( "for mean greater than 62 it is z>4 or 0.00003 </SPAN>\n" );
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