document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162759>Question 1162759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample is drawn from a population with mean μ = 55 and standard deviation σ = 4.6. [You may find it useful to reference the z table.]\r<BR>\n" );
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document.write( "a. Is the sampling distribution of the sample mean with n = 13 and n = 37 normally distributed?\r<BR>\n" );
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document.write( "    Yes, both the sample means will have a normal distribution.<BR>\n" );
document.write( "    No, both the sample means will not have a normal distribution.<BR>\n" );
document.write( "    No, only the sample mean with n = 13 will have a normal distribution.<BR>\n" );
document.write( "    No, only the sample mean with n = 37 will have a normal distribution.\r<BR>\n" );
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document.write( "b. Calculate the probability that the sample mean falls between 55 and 57 for  n = 37. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786598 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=786598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the population is normally distributed, then the sampling distribution of both will be normal.<BR>\n" );
document.write( "If the population is not normally distributed, then it depends. <BR>\n" );
document.write( "Because the z-table is being used, and because sigma and not s is used, I would assume normality in the population and the answer is Yes.\r<BR>\n" );
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document.write( "z=(57-55)/4.6/sqrt(37)<BR>\n" );
document.write( "=2*sqrt(37)/4.6=2.64<BR>\n" );
document.write( "So between 55 (z=0) and 57 (z=2.6446) that probability is 0.4959<BR>\n" );
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