document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200096>Question 1200096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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:<BR>\n" );
document.write( "a. Between the 20th and 50th percentiles.<BR>\n" );
document.write( "b. Between the 40th and 60th percentiles.<BR>\n" );
document.write( "c. Between the 10th and 90th percentiles.<BR>\n" );
document.write( "d. Above the 80th percentile.<BR>\n" );
document.write( "e. Below the 10th percentile.<BR>\n" );
document.write( "f. Above the 5th percentile.	\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848090 by </B><A HREF=/tutors/aboutme.mpl?userid=GingerAle><B>GingerAle(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=GingerAle><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find Z-scores:**\r<BR>\n" );
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document.write( "* **Use a Z-table or calculator (like a TI-84) to find the Z-scores corresponding to the given percentiles.**\r<BR>\n" );
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document.write( "**a. Between 20th and 50th percentiles:**<BR>\n" );
document.write( "    * Z-score for 20th percentile: -0.84<BR>\n" );
document.write( "    * Z-score for 50th percentile: 0 (mean)\r<BR>\n" );
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document.write( "**b. Between 40th and 60th percentiles:**<BR>\n" );
document.write( "    * Z-score for 40th percentile: -0.25<BR>\n" );
document.write( "    * Z-score for 60th percentile: 0.25\r<BR>\n" );
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document.write( "**c. Between 10th and 90th percentiles:**<BR>\n" );
document.write( "    * Z-score for 10th percentile: -1.28<BR>\n" );
document.write( "    * Z-score for 90th percentile: 1.28\r<BR>\n" );
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document.write( "**d. Above 80th percentile:**<BR>\n" );
document.write( "    * Z-score for 80th percentile: 0.84\r<BR>\n" );
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document.write( "**e. Below 10th percentile:**<BR>\n" );
document.write( "    * Z-score for 10th percentile: -1.28\r<BR>\n" );
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document.write( "**f. Above 5th percentile:**<BR>\n" );
document.write( "    * Z-score for 5th percentile: -1.645\r<BR>\n" );
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document.write( "**2. Calculate Heights:**\r<BR>\n" );
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document.write( "* **Use the formula: X = μ + Zσ** <BR>\n" );
document.write( "    * where X is the height, μ is the mean, Z is the z-score, and σ is the standard deviation.\r<BR>\n" );
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document.write( "**a. Between 20th and 50th percentiles:**<BR>\n" );
document.write( "    * 20th percentile: X = 165 + (-0.84)(15) = 151.4 cm<BR>\n" );
document.write( "    * 50th percentile: X = 165 + (0)(15) = 165 cm <BR>\n" );
document.write( "    * Heights: Between 151.4 cm and 165 cm\r<BR>\n" );
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document.write( "**b. Between 40th and 60th percentiles:**<BR>\n" );
document.write( "    * 40th percentile: X = 165 + (-0.25)(15) = 161.25 cm<BR>\n" );
document.write( "    * 60th percentile: X = 165 + (0.25)(15) = 168.75 cm<BR>\n" );
document.write( "    * Heights: Between 161.25 cm and 168.75 cm\r<BR>\n" );
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document.write( "**c. Between 10th and 90th percentiles:**<BR>\n" );
document.write( "    * 10th percentile: X = 165 + (-1.28)(15) = 142.8 cm<BR>\n" );
document.write( "    * 90th percentile: X = 165 + (1.28)(15) = 187.2 cm<BR>\n" );
document.write( "    * Heights: Between 142.8 cm and 187.2 cm\r<BR>\n" );
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document.write( "**d. Above 80th percentile:**<BR>\n" );
document.write( "    * 80th percentile: X = 165 + (0.84)(15) = 177.6 cm<BR>\n" );
document.write( "    * Heights: Above 177.6 cm\r<BR>\n" );
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document.write( "**e. Below 10th percentile:**<BR>\n" );
document.write( "    * 10th percentile: X = 165 + (-1.28)(15) = 142.8 cm<BR>\n" );
document.write( "    * Heights: Below 142.8 cm\r<BR>\n" );
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document.write( "**f. Above 5th percentile:**<BR>\n" );
document.write( "    * 5th percentile: X = 165 + (-1.645)(15) = 139.325 cm<BR>\n" );
document.write( "    * Heights: Above 139.325 cm \r<BR>\n" );
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document.write( "**Note:** These calculations provide approximate values based on the normal distribution. \r<BR>\n" );
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document.write( "Let me know if you'd like to explore any other percentiles or have further questions!<BR>\n" );
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