document.write( "Question 1200428: The mean height of a population of girls aged 15 to 19 years in a certain population was found to be 165 cm with a standard deviation of 15cm. Assuming that the heights are normally distributed, find the heights in centimeters that correspond to the following percentiles:
\n" ); document.write( "a. Between the 20th and 50th percentiles.
\n" ); document.write( "b. Between the 40th and 60th percentiles.
\n" ); document.write( "c. Between the 10th and 90th percentiles.
\n" ); document.write( "d. Above the 80th percentile.
\n" ); document.write( "e. Below the 10th percentile.
\n" ); document.write( "f. Above the 5th percentile.\r
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Algebra.Com's Answer #834581 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "The mean height of a population of girls aged 15 to 19 years in a certain population
\n" ); document.write( "was found to be 165 cm with a standard deviation of 15cm.
\n" ); document.write( "Assuming that the heights are normally distributed, find the heights in centimeters
\n" ); document.write( "that correspond to the following percentiles:
\n" ); document.write( "a. Between the 20th and 50th percentiles.
\n" ); document.write( "b. Between the 40th and 60th percentiles.
\n" ); document.write( "c. Between the 10th and 90th percentiles.
\n" ); document.write( "d. Above the 80th percentile.
\n" ); document.write( "e. Below the 10th percentile.
\n" ); document.write( "f. Above the 5th percentile.
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\n" ); document.write( "\n" ); document.write( "Using function invNorm of TI-83 or TI-84 calculators
\n" ); document.write( "(see the instructions in this web-site https://www.statology.org/invnorm-ti-84/)\r
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document.write( "(a)  Between the 20th and 50th percentiles.\r\n" );
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document.write( "         Find the marks for the given normal curve \r\n" );
document.write( "         corresponding to values of the cumulative probabilities 0.2 and 0.5.\r\n" );
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document.write( "                                                  probability  mean  SD      <<<---=== format\r\n" );
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document.write( "     The lover mark for the height is  invNorm(  0.2,       165,  15) = 152.4 cm  (rounded).\r\n" );
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document.write( "     The upper mark for the height is  invNorm(  0.5,       165,  15) = 165.0 cm  (rounded).\r\n" );
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document.write( "     ANSWER.  The height is  152.4 cm <= h <= 165 cm.\r\n" );
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document.write( "(b), (c) are similar: do them in the same way.\r\n" );
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document.write( "(d)  Above the 80th percentile.\r\n" );
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document.write( "         Find the mark for the given normal curve \r\n" );
document.write( "         corresponding to value of the cumulative probabilities 0.8.\r\n" );
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document.write( "     The mark for the height is  invNorm(  0.8, 165, 15) = 177.6 cm  (rounded).\r\n" );
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document.write( "     ANSWER.  The height is  h >= 177.6 cm.\r\n" );
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document.write( "(e)  Below the 10th percentile.\r\n" );
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document.write( "         Find the mark for the given normal curve \r\n" );
document.write( "         corresponding to value of the cumulative probabilities 0.1.\r\n" );
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document.write( "     The mark for the height is  invNorm(  0.1, 165, 15) = 145.8 cm  (rounded).\r\n" );
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document.write( "     ANSWER.  The height is  h <= 145.8 cm.\r\n" );
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document.write( "(f)  Above the 5th percentile.\r\n" );
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document.write( "         Find the mark for the given normal curve \r\n" );
document.write( "         corresponding to value of the cumulative probabilities 0.05.\r\n" );
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document.write( "     The mark for the height is  invNorm(  0.05, 165, 15) = 140.3 cm  (rounded).\r\n" );
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document.write( "     ANSWER.  The height is  h <= 140.3 cm.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Alternatively, you may use an online calculator at this web-site\r
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\n" ); document.write( "\n" ); document.write( "https://onlinestatbook.com/2/calculators/inverse_normal_dist.html\r
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\n" ); document.write( "\n" ); document.write( "It shows the associated diagrams and makes the entire work more understandable.\r
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\n" ); document.write( "\n" ); document.write( "So, if you are a beginner in study this subject, I recommend you
\n" ); document.write( "to start using this online calculator.\r
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\n" ); document.write( "\n" ); document.write( "Later, when you will learn the subject enough, you may switch to calculators
\n" ); document.write( "TI-83, TI-84 back to be prepared to the exam's environment.\r
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