document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143105>Question 1143105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years (\"Appliance life expectancy,\" 2013).  Assume the life of a dishwasher is normally distributed.\r<BR>\n" );
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document.write( "Using Excel I entered this:\r<BR>\n" );
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document.write( "I am using Excel. An online calculator gives me the answer of 0.054112 and Excel says 0.05548\r<BR>\n" );
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document.write( "d. Find the probability that a dishwasher will last between 8 and 10 years. =SUM(NORM.DIST(10,12,1.25,TRUE)+NORM.DIST(8,12,1.25,TRUE))\r<BR>\n" );
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document.write( "How do I know which is correct? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763880 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=763880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'm not sure how you got the area of .054112 or .05548.<BR>\n" );
document.write( "what was the problem that lead you to those answers?\r<BR>\n" );
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document.write( "the probability that the dishwasher would last between 8 and 10 years should be the area to the left of the z-score associated with the raw score of 10 minus the area to the left of the z-score associated with the raw score of 8.\r<BR>\n" );
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document.write( "your z-scores would be:\r<BR>\n" );
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document.write( "(10 - 12) / 1.25 = -1.6<BR>\n" );
document.write( "(8 - 12) / 1.25 = -3.2\r<BR>\n" );
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document.write( "the area to the left of a z-score of -1.6 = .0547992894<BR>\n" );
document.write( "the area to the left of a z-score of -3.2 = .006872020803\r<BR>\n" );
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document.write( "the area in between = .0547992894 - .006872020803 = .0541120873\r<BR>\n" );
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document.write( "your formula in excel was:\r<BR>\n" );
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document.write( "=SUM(NORM.DIST(10,12,1.25,TRUE)+NORM.DIST(8,12,1.25,TRUE)) \r<BR>\n" );
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document.write( "it should have been:\r<BR>\n" );
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document.write( "=NORM.DIST(10,12,1.25,TRUE) - NORM.DIST(8,12,1.25,TRUE)\r<BR>\n" );
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document.write( "to get the area between 2 z-scores, you subtract the smaller area from the larger area.\r<BR>\n" );
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document.write( "put another way, you subtract the area to the left of the less positive z-score from the area to the left of the higher z-score.\r<BR>\n" );
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document.write( "you added the areas together using the sum function which gave you the wrong answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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