document.write( "Question 1199334: A company that manufactures batteries guarantees them a life of 24 months.
\n" ); document.write( "(i) If the average life has been found in tests to be 33 months and a S. D. of 4 months, how many will have to be replaced under guarantee if a normal distribution is assumed for battery lifetimes ? \n" ); document.write( "

Algebra.Com's Answer #833173 by ikleyn(52898) $\"\"$ $\"About$

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\n" ); document.write( "A company that manufactures batteries guarantees them a life of 24 months.
\n" ); document.write( "If the average life has been found in tests to be 33 months and a S. D. of 4 months,
\n" ); document.write( "how many will have to be replaced under guarantee if a normal distribution
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document.write( "We are given that the lifetime is normally distributed with the mean of 33 months\r\n" );
document.write( "and SD of 4 months.\r\n" );
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document.write( "They want you determine the probability P(L < 24 months), where L is the continuous\r\n" );
document.write( "random variable of lifetime in months.\r\n" );
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document.write( "Every normal distribution curve is a bell shaped curve.\r\n" );
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document.write( "In this problem, they want you determine the area under this specific normal curve\r\n" );
document.write( "on the left from the raw mark of 24 months.  This area is the sought probability.\r\n" );
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document.write( "Go to web-site https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
document.write( "and find there free of charge online calculator, specially developed for this purpose.\r\n" );
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document.write( "Input the mean value 33 and the standard deviation value 4;\r\n" );
document.write( "input 24 in the window \"Below\"; then click \"Recalculate\".\r\n" );
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document.write( "You will get the ANSWER  0.0122  in the window \"Probability\".\r\n" );
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document.write( "The auxiliary plot will show you the area of the interest.\r\n" );
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document.write( "Now, when you know \"what to do\", I will tell you that you can get the same result \r\n" );
document.write( "in other way, using your calculator  TI-83 or TI-84 (or whatever).\r\n" );
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document.write( "For it, use the calculator' standard function normalcdf with parameters\r\n" );
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document.write( "                     z1   z2  mean SD   \r\n" );
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document.write( "     P = normalcdf(-9999, 24,  33, 4) = 0.0122.\r\n" );
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document.write( "You will get the same value of the probability 0.0122 from your calculator.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the solution is completed.\r
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