document.write( "Question 1203821: Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 15.9 years and a standard deviation of 1.4 years. Find the probability that a randomly selected quartz time piece will have a
\n" ); document.write( "replacement time less than 12.1 years? If the company wants to provide a warranty so that only 0.9% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?
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Algebra.Com's Answer #839681 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "Company XYZ \"highlight%28cross%28know%29%29\" knows that replacement times for the quartz time pieces it produces
\n" ); document.write( "are normally distributed with a mean of 15.9 years and a standard deviation of 1.4 years.
\n" ); document.write( "(a) Find the probability that a randomly selected quartz time piece will have a
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\n" ); document.write( "(b) If the company wants to provide a warranty so that only 0.9% of the quartz time pieces
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document.write( "(a)  In part (a), they want you determine the probability that a randomly selected quartz \r\n" );
document.write( "     time piece will have a replacement time less than 12.1 years.\r\n" );
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document.write( "     It is the same as to determine the area under the given normal curve \r\n" );
document.write( "     on the left of the time mark of 12.1 year.\r\n" );
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document.write( "     Use the standard function normalcdf of your regular calculator TI-83/84\r\n" );
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document.write( "                         z1    z2    mean   SD    <<<---===  formatting pattern\r\n" );
document.write( "         P = normalcdf(-9999, 12.1,  15.9,  1.4)\r\n" );
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document.write( "     You will get the value P = 0.0033  (rouned).    ANSWER\r\n" );
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document.write( "     Alternatively, you may use free of charge online calculator at this web-site\r\n" );
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document.write( "         https://davidmlane.com/hyperstat/z_table.html\r\n" );
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document.write( "     (use it in the mode \"Area from a value\").\r\n" );
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document.write( "     It has clearly designed interface, so even a beginner student can learn it and use easily.\r\n" );
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document.write( "     Online calculator will give you the same answer.\r\n" );
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document.write( "(b)  In part (b), they want you determine the time mark on the number line such that\r\n" );
document.write( "     only 0.9% = 0.009 of the quartz time pieces will be replaced before the warranty expires.\r\n" );
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document.write( "     It is the same as to determine the time mark on the number line such that \r\n" );
document.write( "     the area under the normal curve on the left of this mark would be 0.009.\r\n" );
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document.write( "     Use the standard function invNorm of your regular calculator TI-83/84\r\n" );
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document.write( "                          area    mean   SD    <<<---===  formatting pattern\r\n" );
document.write( "         years = invNorm(0.009,  15.9,  1.4)\r\n" );
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document.write( "     You will get the value years = 13.534,  or 13.5 years,  rounded.    ANSWER\r\n" );
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document.write( "     Alternatively, you may use the same free of charge online calculator at this web-site\r\n" );
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document.write( "         https://davidmlane.com/hyperstat/z_table.html\r\n" );
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document.write( "     (this time use it in the mode \"Value from an area\").\r\n" );
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document.write( "\r\n" );
document.write( "     It has clearly designed interface, so even a beginner student can learn it and use easily.\r\n" );
document.write( "\r\n" );
document.write( "     Online calculator will give you the same answer.\r\n" );
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