document.write( "Question 969359: A company knows that replacement times for the DVD players it produces are Normally distributed with a mean of 4.3 years and a standard deviation of 2.4 years.\r
\n" ); document.write( "\n" ); document.write( "If the company wants to provide a warranty so that only 2.9% of the DVD players will be replaced before the warranty expires, what is the time length of the warranty? \r
\n" ); document.write( "\n" ); document.write( "Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. \n" ); document.write( "
Algebra.Com's Answer #592261 by Boreal(15235)\"\" \"About 
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With 2 SDs, it would be 9.1 days, and 97.1% working is very close to 97.5%, so I would expect the number to be close to 9.1 days, but a littleness.\r
\n" ); document.write( "\n" ); document.write( "Using a z-table or a calculator, 0.971 on the z-table (0.029) is with a z-score of 1.895 (at 1.89, the z-score is 0.9706 and at 1.90 it is 0.9713). \r
\n" ); document.write( "\n" ); document.write( "z=(Value-mean)/SD
\n" ); document.write( "1.895=Value-4.3/2.4 Multiply by 2.4
\n" ); document.write( "4.548=Value-4.3 Add 4.3
\n" ); document.write( "8.848=Value or 8.8 days.\r
\n" ); document.write( "\n" ); document.write( "Check
\n" ); document.write( "(8.8-4.3)/2.4 = z= (4.5/2.4)=1.875. This rounds to 0.970.
\n" ); document.write( "(8.9-4.3)/2.4=z=1.917 This rounds to 0.972.
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