document.write( "Question 1184845: A manufacturer knows that their items have a normally distributed lifespan,
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\n" ); document.write( "\n" ); document.write( "If you randomly purchase 22 items, what is the probability that their mean
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Algebra.Com's Answer #815490 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
A manufacturer knows that their items have a normally distributed lifespan,
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\n" ); document.write( "life will be longer than 15 years? (Give answer to 4 decimal places.)
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document.write( "The rule is:\r\n" );
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document.write( "You must use the t-distribution when working problems when the population\r\n" );
document.write( "standard deviation (σ) is not known and the sample size is small (n<30).\r\n" );
document.write( "General Correct Rule: If σ is not known, then using t-distribution is\r\n" );
document.write( "correct. If σ is known, then using the normal distribution is correct.\r\n" );
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document.write( "In this problem, σ is known, so we use the normal distribution.  However,\r\n" );
document.write( "since the sample size is 22 we must divide the standard deviation by √22.\r\n" );
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document.write( "On your TI-84, press ON CLEAR 2ND VARS 3\r\n" );
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document.write( "Make the screen read like this:\r\n" );
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document.write( "     normalcdf\r\n" );
document.write( "lower:15\r\n" );
document.write( "upper:99999999\r\n" );
document.write( "μ:13.9\r\n" );
document.write( "σ:2/√(22)      <-- the √ key is 2ND x2\r\n" );
document.write( "Paste\r\n" );
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document.write( "Use the down arrow key to highlight Paste\r\n" );
document.write( "Press ENTER\r\n" );
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document.write( "Read this:\r\n" );
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document.write( "normalcdf(15,13.9,2/√(22))\r\n" );
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document.write( "Press ENTER\r\n" );
document.write( " \r\n" );
document.write( "Read 0.0049439287\r\n" );
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document.write( "Round to 0.0049\r\n" );
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document.write( "Edwin
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