document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137215>Question 1137215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A normal distribution has μ = 30 and σ = 5.<BR>\n" );
document.write( "(a) Find the z score corresponding to <BR>\n" );
document.write( "x = 25.<BR>\n" );
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document.write( "(b) Find the z score corresponding to <BR>\n" );
document.write( "x = 44.<BR>\n" );
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document.write( "(c) Find the raw score corresponding to <BR>\n" );
document.write( "z = −3.<BR>\n" );
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document.write( "(d) Find the raw score corresponding to <BR>\n" );
document.write( "z = 1.7.<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 #755076 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=755076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\">I'll do part (a) and part (c) as they are different problems; while (b) and (d) are similar to (a) and (c), so I'll leave those for you to try out.\r<BR>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "Plug in x = 25, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+30 ALIGN=MIDDLE  ALT=\"mu+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+5 ALIGN=MIDDLE  ALT=\"sigma+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Compute to find z.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28x-mu%29%2F%28sigma%29 ALIGN=MIDDLE  ALT=\"z+=+%28x-mu%29%2F%28sigma%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%2825-30%29%2F%285%29 ALIGN=MIDDLE  ALT=\"z+=+%2825-30%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28-5%29%2F%285%29 ALIGN=MIDDLE  ALT=\"z+=+%28-5%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-1 ALIGN=MIDDLE  ALT=\"z+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The z score is z = -1\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "Plug in z = -3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+30 ALIGN=MIDDLE  ALT=\"mu+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+5 ALIGN=MIDDLE  ALT=\"sigma+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28x-mu%29%2F%28sigma%29 ALIGN=MIDDLE  ALT=\"z+=+%28x-mu%29%2F%28sigma%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3+=+%28x-30%29%2F%285%29 ALIGN=MIDDLE  ALT=\"-3+=+%28x-30%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28-3%29+=+5%2A%28x-30%29%2F%285%29 ALIGN=MIDDLE  ALT=\"5%28-3%29+=+5%2A%28x-30%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15+=+x-30 ALIGN=MIDDLE  ALT=\"-15+=+x-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-30+=+-15 ALIGN=MIDDLE  ALT=\"x-30+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-30%2B30+=+-15%2B30 ALIGN=MIDDLE  ALT=\"x-30%2B30+=+-15%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 30 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The raw score is x = 15. \r<BR>\n" );
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document.write( "Note that if you plugged x = 15 into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28x-mu%29%2F%28sigma%29 ALIGN=MIDDLE  ALT=\"z+=+%28x-mu%29%2F%28sigma%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, similar to part (a), then you should get z = -3 which helps confirm the answer.</font> </SPAN>\n" );
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