document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181630>Question 1181630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A distribution of values is normal with a mean of 49.7 and a standard deviation of 25.\r<BR>\n" );
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document.write( "Find P70, which is the score separating the bottom 70% from the top 30%. \r<BR>\n" );
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document.write( "P70 = \r<BR>\n" );
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document.write( "Enter your answer as a number accurate to 4 decimal places.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849989 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=849989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to find P70:\r<BR>\n" );
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document.write( "1. **Find the z-score:** P70 represents the 70th percentile. We need to find the z-score that corresponds to a cumulative probability of 0.70. You can use a z-table or a calculator with statistical functions for this. The z-score for 0.70 is approximately 0.52.\r<BR>\n" );
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document.write( "2. **Use the z-score formula:** The z-score formula is:\r<BR>\n" );
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document.write( "   z = (x - μ) / σ\r<BR>\n" );
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document.write( "   Where:<BR>\n" );
document.write( "   * z is the z-score<BR>\n" );
document.write( "   * x is the value we're looking for (P70)<BR>\n" );
document.write( "   * μ is the mean (49.7)<BR>\n" );
document.write( "   * σ is the standard deviation (25)\r<BR>\n" );
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document.write( "3. **Solve for x (P70):**\r<BR>\n" );
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document.write( "   0.52 = (x - 49.7) / 25\r<BR>\n" );
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document.write( "   Multiply both sides by 25:\r<BR>\n" );
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document.write( "   13 = x - 49.7\r<BR>\n" );
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document.write( "   Add 49.7 to both sides:\r<BR>\n" );
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document.write( "   x = 62.7\r<BR>\n" );
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document.write( "Therefore, P70 ≈ 62.7000<BR>\n" );
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