document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192122>Question 1192122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey showed that 71% of adults need some form of vision correction (eyeglasses, contacts, surgery, etc.). Suppose 9 adults are randomly selected, and 8 of them turn out to need some form of vision correction. Is 8 a significantly high number of adults who need vision correction out of 9 randomly selected adults? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849085 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=849085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to determine if 8 out of 9 adults needing vision correction is significantly high:\r<BR>\n" );
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document.write( "1. **Define \"Significantly High\":**  We need to establish a threshold for what we consider \"significantly high.\"  A common approach is to use the range rule of thumb, which considers values outside of two standard deviations from the mean as significantly different.\r<BR>\n" );
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document.write( "2. **Calculate the Mean (μ):**\r<BR>\n" );
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document.write( "   μ = n * p = 9 * 0.71 = 6.39\r<BR>\n" );
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document.write( "3. **Calculate the Standard Deviation (σ):**\r<BR>\n" );
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document.write( "   σ = sqrt(n * p * (1-p)) = sqrt(9 * 0.71 * 0.29) ≈ 1.36\r<BR>\n" );
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document.write( "4. **Calculate the Range of Usual Values:**\r<BR>\n" );
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document.write( "   * Lower Bound: μ - 2σ = 6.39 - 2 * 1.36 ≈ 3.67<BR>\n" );
document.write( "   * Upper Bound: μ + 2σ = 6.39 + 2 * 1.36 ≈ 9.11\r<BR>\n" );
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document.write( "5. **Compare the Observed Value:**\r<BR>\n" );
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document.write( "   The observed value is 8.\r<BR>\n" );
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document.write( "6. **Make a Decision:**\r<BR>\n" );
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document.write( "   Since 8 falls within the range of usual values (3.67 to 9.11), it is *not* considered significantly high.\r<BR>\n" );
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document.write( "**Conclusion:**\r<BR>\n" );
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document.write( "8 adults needing vision correction out of 9 randomly selected adults is within the expected range based on the given probability.  Therefore, it is not considered a significantly high number.<BR>\n" );
document.write( " </SPAN>\n" );
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