document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192261>Question 1192261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district, based on the scores on a reading achievement exam. The average score is found to be 122.6 with a standard deviation of 18. Assume that the variable is normally distributed.What is the 75th percentile score? Write your answer to the nearest whole number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849062 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to find the 75th percentile score:\r<BR>\n" );
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document.write( "**1. Understand Percentiles and Z-scores**\r<BR>\n" );
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document.write( "* The 75th percentile is the score below which 75% of the data falls.<BR>\n" );
document.write( "* Z-scores measure how many standard deviations a particular score is away from the mean.\r<BR>\n" );
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document.write( "**2. Find the Z-score for the 75th Percentile**\r<BR>\n" );
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document.write( "You can use a Z-table or a calculator with statistical functions to find the Z-score corresponding to the 75th percentile (0.75). The Z-score is approximately 0.67.\r<BR>\n" );
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document.write( "**3. Use the Z-score Formula**\r<BR>\n" );
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document.write( "The formula to convert a Z-score to a raw score (the actual test score) is:\r<BR>\n" );
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document.write( "X = μ + (Z * σ)\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* X is the raw score you're trying to find<BR>\n" );
document.write( "* μ is the mean of the distribution (122.6)<BR>\n" );
document.write( "* σ is the standard deviation (18)<BR>\n" );
document.write( "* Z is the Z-score (0.67)\r<BR>\n" );
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document.write( "**4. Calculate**\r<BR>\n" );
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document.write( "X = 122.6 + (0.67 * 18)<BR>\n" );
document.write( "X = 122.6 + 12.06<BR>\n" );
document.write( "X = 134.66\r<BR>\n" );
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document.write( "**5. Round**\r<BR>\n" );
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document.write( "Rounding to the nearest whole number, the 75th percentile score is 135.<BR>\n" );
document.write( " </SPAN>\n" );
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