document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258722>Question 258722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Normal Distribution<BR>\n" );
document.write( "The scores for the intelligence quotient (IQ) test are normally distributed with mean 100 and standard deviation 16. <BR>\n" );
document.write( "(a) What is the probability that at least two of five randomly selected people have IQ test score higher than 120? <BR>\n" );
document.write( "(b) A person is randomly selected from all people whose IQ are higher than 110. What is the probability that this person has IQ higher than 120? <BR>\n" );
document.write( "(c) One thousand people are randomly selected. Approximately what is the probability that fewer than 90 of them have IQ score higher than 120? </SPAN>\n" );
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document.write( "The scores for the intelligence quotient (IQ) test are normally distributed with mean 100 and standard deviation 16. <BR>\n" );
document.write( "(a) What is the probability that at least two of five randomly selected people have IQ test score higher than 120? <BR>\n" );
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document.write( "Find the z-score of 120:<BR>\n" );
document.write( "z(120) = (120-100)/16 = 1.25<BR>\n" );
document.write( "P(z>1.25) = normalcdf(1.25,100) = 0.1056<BR>\n" );
document.write( "Find P(2<= x <=5 with n = 5 and p = 0.1056) = 1-binomcdf(5,0.1056,1) = 0.0899..<BR>\n" );
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document.write( "(b) A person is randomly selected from all people whose IQ are higher than 110. What is the probability that this person has IQ higher than 120?<BR>\n" );
document.write( "z(110) = 10/16 = 0.625<BR>\n" );
document.write( "P(x>110) = P(z> 0.625) = 0.26598..<BR>\n" );
document.write( "P(x>120 | x>110) = P(x > 120)/P(x>110) = 0.1056/0.26598 = 0.3970..<BR>\n" );
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document.write( "(c) One thousand people are randomly selected. Approximately what is the probability that fewer than 90 of them have IQ score higher than 120?<BR>\n" );
document.write( "P(x>120) = 0.1056<BR>\n" );
document.write( "P(k< 90) = binomcdf(1000,0.1056,89) = 0.04624.....<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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