document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170955>Question 1170955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> IQ is normally distributed with a mean of 100 and a standard deviation of 15.\r<BR>\n" );
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document.write( "a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95.<BR>\n" );
document.write( "Write your answer in percent form. Round to the nearest tenth of a percent.<BR>\n" );
document.write( "P<BR>\n" );
document.write( "P<BR>\n" );
document.write( " (IQ greater than 95) = %<BR>\n" );
document.write( "b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. <BR>\n" );
document.write( "Write your answer in percent form. Round to the nearest tenth of a percent.<BR>\n" );
document.write( "P<BR>\n" );
document.write( "P<BR>\n" );
document.write( " (IQ less than 125) = %<BR>\n" );
document.write( "c) In a sample of 600 people, how many people would have an IQ less than 110?<BR>\n" );
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document.write( "d) In a sample of 600 people, how many people would have an IQ greater than 140?<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 #851030 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=851030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve each part of the problem:\r<BR>\n" );
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document.write( "**Given:**\r<BR>\n" );
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document.write( "* Mean (μ) = 100<BR>\n" );
document.write( "* Standard deviation (σ) = 15<BR>\n" );
document.write( "* IQ is normally distributed.\r<BR>\n" );
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document.write( "**a) Probability of IQ greater than 95:**\r<BR>\n" );
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document.write( "1.  **Calculate the z-score:**<BR>\n" );
document.write( "    * z = (x - μ) / σ<BR>\n" );
document.write( "    * z = (95 - 100) / 15 = -5 / 15 = -1/3 ≈ -0.3333\r<BR>\n" );
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document.write( "2.  **Find the probability:**<BR>\n" );
document.write( "    * Use a z-table or calculator to find P(Z > -0.3333).<BR>\n" );
document.write( "    * P(Z > -0.3333) = 1 - P(Z < -0.3333) ≈ 1 - 0.3707 ≈ 0.6293\r<BR>\n" );
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document.write( "3.  **Convert to percentage and round:**<BR>\n" );
document.write( "    * 0.6293 * 100 = 62.93%<BR>\n" );
document.write( "    * Rounded to the nearest tenth: 62.9%\r<BR>\n" );
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document.write( "**b) Probability of IQ less than 125:**\r<BR>\n" );
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document.write( "1.  **Calculate the z-score:**<BR>\n" );
document.write( "    * z = (125 - 100) / 15 = 25 / 15 = 5/3 ≈ 1.6667\r<BR>\n" );
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document.write( "2.  **Find the probability:**<BR>\n" );
document.write( "    * Use a z-table or calculator to find P(Z < 1.6667).<BR>\n" );
document.write( "    * P(Z < 1.6667) ≈ 0.9525\r<BR>\n" );
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document.write( "3.  **Convert to percentage and round:**<BR>\n" );
document.write( "    * 0.9525 * 100 = 95.25%<BR>\n" );
document.write( "    * Rounded to the nearest tenth: 95.3%\r<BR>\n" );
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document.write( "**c) Number of people with IQ less than 110 in a sample of 600:**\r<BR>\n" );
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document.write( "1.  **Calculate the z-score:**<BR>\n" );
document.write( "    * z = (110 - 100) / 15 = 10 / 15 = 2/3 ≈ 0.6667\r<BR>\n" );
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document.write( "2.  **Find the probability:**<BR>\n" );
document.write( "    * Use a z-table or calculator to find P(Z < 0.6667).<BR>\n" );
document.write( "    * P(Z < 0.6667) ≈ 0.7475\r<BR>\n" );
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document.write( "3.  **Calculate the expected number:**<BR>\n" );
document.write( "    * Expected number = 600 * 0.7475 ≈ 448.5<BR>\n" );
document.write( "    * Rounded to the nearest whole number: 449\r<BR>\n" );
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document.write( "**d) Number of people with IQ greater than 140 in a sample of 600:**\r<BR>\n" );
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document.write( "1.  **Calculate the z-score:**<BR>\n" );
document.write( "    * z = (140 - 100) / 15 = 40 / 15 = 8/3 ≈ 2.6667\r<BR>\n" );
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document.write( "2.  **Find the probability:**<BR>\n" );
document.write( "    * Use a z-table or calculator to find P(Z > 2.6667).<BR>\n" );
document.write( "    * P(Z > 2.6667) = 1 - P(Z < 2.6667) ≈ 1 - 0.9962 ≈ 0.0038\r<BR>\n" );
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document.write( "3.  **Calculate the expected number:**<BR>\n" );
document.write( "    * Expected number = 600 * 0.0038 ≈ 2.28<BR>\n" );
document.write( "    * Rounded to the nearest whole number: 2\r<BR>\n" );
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document.write( "**Answers:**\r<BR>\n" );
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document.write( "* a) P(IQ greater than 95) = 62.9%<BR>\n" );
document.write( "* b) P(IQ less than 125) = 95.3%<BR>\n" );
document.write( "* c) 449 people<BR>\n" );
document.write( "* d) 2 people<BR>\n" );
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