document.write( "Question 1199349: The average speed of a certain biplane is 117.9 miles/hour.
\n" ); document.write( "85% of these biplanes have a speed not greater than 131 miles/hour.
\n" ); document.write( "This is a normal distribution.
\n" ); document.write( "Use your graphing calculator to find the standard deviation. \n" ); document.write( "

Algebra.Com's Answer #833199 by ikleyn(52839) $\"\"$ $\"About$

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\n" ); document.write( "The average speed of a certain biplane is 117.9 miles/hour.
\n" ); document.write( "85% of these biplanes have a speed not greater than 131 miles/hour.
\n" ); document.write( "This is a normal distribution.
\n" ); document.write( "Use your graphing calculator to find the standard deviation.
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document.write( "We will use the condition \"85% of these biplanes have a speed not greater than 131 miles/hour\"\r\n" );
document.write( "to find the raw score on this specified normal curve, that corresponds to 85% of these biplanes.\r\n" );
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document.write( "  |  This score, when expressed/measured as a raw score on the specified normal curve,    |\r\n" );
document.write( "  |  has its specific value; but when measured in terms of the standard deviation,        |\r\n" );
document.write( "  |  it is the same as the standard z-score of the 85% area on the standard normal curve. |\r\n" );
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document.write( "      / It is the major knowledge you need to know when solving such problems. /\r\n" );
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document.write( "So, we first determine the standard z-score on the standard normal curve, using the condition\r\n" );
document.write( "that 85% of the area under the standard normal curve is on the left of this standard score.\r\n" );
document.write( "So, use the invNorm function of the graphing calculator in this format\r\n" );
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document.write( "                               area    mean  SD\r\n" );
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document.write( "    standard z-score = invNorm(0.85,    0,    1) = 1.036433.\r\n" );
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document.write( "Now, we know that this standard z-score of 1.036433 is the same as the raw z-score\r\n" );
document.write( "expressed in terms of the standard deviation\r\n" );
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document.write( "    1.036433 =  = .\r\n" );
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document.write( "In this equation, only SD (the standard deviation) is the unknown, so we easily find it\r\n" );
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document.write( "    1.036433*SD = 131-117.9 = 13.1\r\n" );
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document.write( "             SD = 13.1/1.036433 = 12.6395   (rounded).\r\n" );
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document.write( "ANSWER.  The standard deviation is 12.6395 miles.\r\n" );
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