document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076540>Question 1076540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume, L litres, of emulsion paint in a plastic tub may be assumed to be normally distributed with mean 10.25 and variance s2.<BR>\n" );
document.write( "(a) Assuming that s2   0.04, determine P(L<10) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691167 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=691167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the volume is a normal distribution with mean = 10.25 and variance = s^2 (?)\r<BR>\n" );
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document.write( "if s^2 = .04, then s = sqrt(.04) = .2\r<BR>\n" );
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document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "m =10.25<BR>\n" );
document.write( "s = .2\r<BR>\n" );
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document.write( "you want to find the probability of the number of liters being 10 or less.\r<BR>\n" );
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document.write( "you calculate the z-factors as follows:\r<BR>\n" );
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document.write( "z = (x-m)/s\r<BR>\n" );
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document.write( "z is the z-factor<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is raw mean<BR>\n" );
document.write( "s is the standared deviation\r<BR>\n" );
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document.write( "you get z = (10 - 10.25) / .2\r<BR>\n" );
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document.write( "solve for z to get z = -.25 / .2 = -.125\r<BR>\n" );
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document.write( "use a z-score calculator or a z-score table to find the area to the left of a z-score of -.125.\r<BR>\n" );
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document.write( "i used the the following calculator.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://stattrek.com/online-calculator/normal.aspx\" target = \"_blank\">http://stattrek.com/online-calculator/normal.aspx</a>\r<BR>\n" );
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document.write( "i used the following table.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\" target = \"_blank\">http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf</a>\r<BR>\n" );
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document.write( "i entered a z-score of -.125.<BR>\n" );
document.write( "the mean is and the standard deviation is 1 for a z-score.<BR>\n" );
document.write( "the calculator then told me that the  probability of getting a z-score to the left of that (less than that) was .45026\r<BR>\n" );
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document.write( "the calculator told me that the probability of a z-score being less than -.125 is .45026\r<BR>\n" );
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document.write( "with the table, i had to do a little interpolating.\r<BR>\n" );
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document.write( "this is because the table only goes to 2 decimal places.\r<BR>\n" );
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document.write( "i looked for the probability to the left of -.12 and to the left of -.13.\r<BR>\n" );
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document.write( "a z-score of -.12 gave an area to the left as .4522.\r<BR>\n" );
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document.write( "a z-score of -.13 gave an area to the left as .4483.\r<BR>\n" );
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document.write( "since -.125 is roughly in between, then i calculated that the probability would be .45025\r<BR>\n" );
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document.write( "the calculator is more accurate than interpolation because interpolation is straight line while the actual values in between are more on a curve.\r<BR>\n" );
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document.write( "here's a picture of what the calculator shows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/041401.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "here's a picture of what the correct row on the table shows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/041402.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/041403.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "in the table, the first column gets you to the row that contains a z-score of -.1.\r<BR>\n" );
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document.write( "that's one decimal place accuracy only.\r<BR>\n" );
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document.write( "on that same row, the third column gets you the area to the left of a z-score of -.12 and the fourth column gets you to the area to the left of a z-score of -.13.\r<BR>\n" );
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document.write( "that's twodecimal place accuracy only.\r<BR>\n" );
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document.write( "you then interpolate to get the area to the left of a z-score of -.125\r<BR>\n" );
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document.write( " </SPAN>\n" );
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