document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190332>Question 1190332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The mean useful life of car batteries is 55 months. They have a standard deviation of 2. Assume the useful life of batteries is normally distributed.\r<BR>\n" );
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document.write( "a. Calculate the percent of batteries with a useful life of less than 51 months. (Round your answer to the nearest hundredth percent.)<BR>\n" );
document.write( "b. Calculate the percent of batteries that will last longer than 61 months. (Round your answer to the nearest hundredth percent.)\r<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 #821953 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=821953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 55<BR>\n" );
document.write( "standard deviation = 2<BR>\n" );
document.write( "z-score = (x - m) / s<BR>\n" );
document.write( "x = the raw score = 51<BR>\n" );
document.write( "m = the mean = 55<BR>\n" );
document.write( "s = standard deviation = 2\r<BR>\n" );
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document.write( "for part a ....\r<BR>\n" );
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document.write( "z = (x - m) / s becomes z = (51 - 55) / 2 = -4 / 2 = -2<BR>\n" );
document.write( "area to the left of z-score of -2 = .02275<BR>\n" );
document.write( "rounded to 4 decimal places to bet .0228 = 2.28%.\r<BR>\n" );
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document.write( "for part b ....\r<BR>\n" );
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document.write( "z = (x - m) / s becomes z = (61 - 55) / 2 = 6/2 = 3<BR>\n" );
document.write( "area to the left of z-score of 3 = .99865.<BR>\n" );
document.write( "area to the right of z-score of 3 = 1 - .99865 = .00135.<BR>\n" );
document.write( "round to 4 decimal places to get .0014 = .14%.\r<BR>\n" );
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document.write( "i used the following z-score table to get these figures.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf\" target = \"_blank\">https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf</a>\r<BR>\n" );
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document.write( "using the ti-85 plus calculator, i got:\r<BR>\n" );
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document.write( "area to the left of z-score of -2 = .022750062.<BR>\n" );
document.write( "rounded to 4 decimal places = .0228 = 2.28%.\r<BR>\n" );
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document.write( "area to the left of z-score of 3 = .9986500328.<BR>\n" );
document.write( "area to the right of z-score of 3 = 1 minus .9986500328 = .0013499672.<BR>\n" );
document.write( "rounded to 4 decimal places = .0013 = .13%.\r<BR>\n" );
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document.write( "the discrepancy between .13% and .14% has to do with the table figures being rounded to 5 decimal places while the calculator figures are being rounded to 7 or 8 decimal places.<BR>\n" );
document.write( "the difference affected the rounding to 4 decimal places in this case.<BR>\n" );
document.write( "it's a small difference, but it is a difference.<BR>\n" );
document.write( "if you go by the table, then .14% is more accurate.\r<BR>\n" );
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