document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=456928>Question 456928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me to solve this  part question.\r<BR>\n" );
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document.write( "Must show work.\r<BR>\n" );
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document.write( "	A population has a normal distribution with a mean of 130 and a standard deviation of 30. Find the probability that a single element selected from the population will have a value between 139.50 and 167.25. <BR>\n" );
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document.write( "	Use the population described in problem 2 above. Now find the probability that the sample mean for a sample of 16 elements selected from the population will be between 139.50 and 167.25. 			<BR>\n" );
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document.write( "	Explain the reason the answers to the above are different.\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 #313592 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=313592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A population has a normal distribution with a mean of 130 and a standard deviation of 30. Find the probability that a single element selected from the population will have a value between 139.50 and 167.25.<BR>\n" );
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document.write( "z(139.5)=(139.5-130)/30 = 0.3167<BR>\n" );
document.write( "z(167.25)=(167.25-130)/30 = 1.2417<BR>\n" );
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document.write( "P(139.5< x < 167.25) = P(0.3167< z <1.2417) = 0.2686<BR>\n" );
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document.write( "Use the population described in problem 2 above. Now find the probability that the sample mean for a sample of 16 elements selected from the population will be between 139.50 and 167.25.<BR>\n" );
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document.write( "t(139.5)=(139.5-130)/[30/sqrt(16)] = 1.2667<BR>\n" );
document.write( "t(167.25)=(167.25-130)/[30/sqrt(16)] = 4.9667<BR>\n" );
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document.write( "P(139.5 < x-bar < 167.25) = P(1.2667 < t < 4.9667 when df = 15) = 0.1122<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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