document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207168>Question 1207168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -2.572°C and -0.181°C </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844886 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=844886\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is 0 and the standard deviation is 1 degrees<BR>\n" );
document.write( "the probabiliy you'll get a reading between -2.572 degrees and -0.181 degrees can be found using the z-score as follows.\r<BR>\n" );
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document.write( "z-score formuls is z = (x-m)/s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the critical low score or the critical high score.<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "using the low score, the formula becomes z = (-2.572 - 0) / 1 = -2.572.<BR>\n" );
document.write( "using the high score, the formula becomes z = -.181 - 0) / 1 = -.181.\r<BR>\n" );
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document.write( "you can use a z-score calculator to find that the area to the left of the z-score of -2.572 is equal to .0050556733 and the area to the left of the z-score of -.181 is equal to .428183948.<BR>\n" );
document.write( "the area in between is the larger area minus the smaller area equal to .4231281215.\r<BR>\n" );
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document.write( "that's the probability that the temperature will be between -2.572 degrees and -.181 degrees centigrade.\r<BR>\n" );
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document.write( "some calculators allow you to find it directly, without having to use the z-scorfes.\r<BR>\n" );
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document.write( "one such calculator canb e found at <a  rel=nofollow HREF= \"https://www.hackmath.net/en/calculator/normal-distribution?mean=3510&sd=25&above=3485&area=below&below=3485&ll=&ul=&outsideLL=&outsideUL=&draw=Calculate\" target = \"_blank\">https://www.hackmath.net/en/calculator/normal-distribution?mean=3510&sd=25&above=3485&area=below&below=3485&ll=&ul=&outsideLL=&outsideUL=&draw=Calculate</a>\r<BR>\n" );
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document.write( "with this calculator, you enter the mean and the standard deviation and the low and high score desired and it tells you the probability.\r<BR>\n" );
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document.write( "here are the results.\r<BR>\n" );
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document.write( "if you wanted the z-score, rather than the raw score, you would have entered a mean of 0 and a standard deviation of 1.\r<BR>\n" );
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document.write( "this problem is unique in that the z-score has a mean of 0 and a standard deviation of 1 and also has a raw score with a mean of 0 and a standard deviation of 1.<BR>\n" );
document.write( "that is not usually the case.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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