document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274080>Question 274080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47.  I need to determine the value of x from the following information:<BR>\n" );
document.write( "a) 60% fo the values are greater than x<BR>\n" );
document.write( "b) x is less than 17% of the values<BR>\n" );
document.write( "c) 22% of the values are less than x<BR>\n" );
document.write( "d) x is greater than 55% of the values.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200083 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=200083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. I need to determine the value of x from the following information:<BR>\n" );
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document.write( "Please draw a picture of the normal curve so you can see what<BR>\n" );
document.write( "these problems are asking you to find.<BR>\n" );
document.write( "Put 200 at the middle mark and note that sigma = 47.<BR>\n" );
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document.write( "a) 60% of the values are greater than x<BR>\n" );
document.write( "So you want a right tail that has 60% of the area in it.<BR>\n" );
document.write( "1st: Find the z-value that marks off that region:<BR>\n" );
document.write( "invNorm(0.4) = -0.2533<BR>\n" );
document.write( "2nd: Find the corresponding \"x\" value using<BR>\n" );
document.write( "x = z*sigma + u<BR>\n" );
document.write( "x = -0.2533*47 + 200<BR>\n" );
document.write( "x = 188.09<BR>\n" );
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document.write( "b) x is less than 17% of the values<BR>\n" );
document.write( "Right-tail has 17% of the area<BR>\n" );
document.write( "z value = invNorm(0.83) = 0.9542<BR>\n" );
document.write( "x value = 0.9542*47+200 = 244.85<BR>\n" );
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document.write( "c) 22% of the values are less than x<BR>\n" );
document.write( "Left-tail of 22%<BR>\n" );
document.write( "z-value = invNorm(0.22) = -0.7722<BR>\n" );
document.write( "x-value = -0.7722*47+200 = 163.71<BR>\n" );
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document.write( "d) x is greater than 55% of the values<BR>\n" );
document.write( "Left-tail of 55%<BR>\n" );
document.write( "z-value = invNorm(0.55) = 0.1257<BR>\n" );
document.write( "x-value = 0.1257*47+200 = 205.91<BR>\n" );
document.write( "=============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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