document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196426>Question 1196426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain brand of light bulb has a mean life of 600 hours and a standard deviation of 53 hours.\r<BR>\n" );
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document.write( "Assuming the data are bell-shaped, what percentage of these light bulbs will have a life between 547 and 706 hours?\r<BR>\n" );
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document.write( "Group of answer choices\r<BR>\n" );
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document.write( "95%\r<BR>\n" );
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document.write( "18.5%\r<BR>\n" );
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document.write( "68%\r<BR>\n" );
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document.write( "81.5%\r<BR>\n" );
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document.write( "13.5% </SPAN>\n" );
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document.write( "\"bell shaped\" is another way of saying we have a normal distribution. Some textbooks will call it a Gaussian curve.\r<BR>\n" );
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document.write( "mu = 600  = mean<BR>\n" );
document.write( "sigma = 53 = standard deviation\r<BR>\n" );
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document.write( "Let's compute the z score for x = 547<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (547-600)/53<BR>\n" );
document.write( "z = -53/53<BR>\n" );
document.write( "z = -1<BR>\n" );
document.write( "This score is exactly one standard deviation below the mean.\r<BR>\n" );
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document.write( "Repeat for x = 706<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (706-600)/53<BR>\n" );
document.write( "z = 106/53<BR>\n" );
document.write( "z = 2<BR>\n" );
document.write( "This score is exactly two standard deviations above the mean\r<BR>\n" );
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document.write( "The task of finding P(547 < x < 706) is the same as P(-1 < z < 2) for this problem's context.\r<BR>\n" );
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document.write( "Let's turn to the Empirical Rule<BR>\n" );
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document.write( "We'll be adding the two pink 34% regions, and the right-hand region of 13.5 in blue<BR>\n" );
document.write( "These three regions span from z = -1 to z = 2<BR>\n" );
document.write( "0.34+0.34+0.135 = 0.815\r<BR>\n" );
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document.write( "According to the Empirical Rule<BR>\n" );
document.write( "P(-1 < z < 2) = 0.815 approximately<BR>\n" );
document.write( "which translates back to<BR>\n" );
document.write( "P(547 < x < 706) = 0.815 approximately when mu = 600 and sigma = 53\r<BR>\n" );
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document.write( "This means roughly 81.5% of the light bulbs have a lifespan between 547 hours and 706 hours.\r<BR>\n" );
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document.write( "Answer: 81.5% (choice C)<BR>\n" );
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document.write( " </SPAN>\n" );
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