document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=347582>Question 347582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1-the graduate selection committee wants to select the top 10% of applicants. On a standardized test with a mean of 500 and a standard diviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that test is normally distributed?<BR>\n" );
document.write( "2- The average commute time via train from the chicago O'Hare Airport to downtown is 60 minutes with a s=15 minutes.Assume that the commute times are normally distributed. what proportion of communtes would be:<BR>\n" );
document.write( "a. Longer than 80 minutes?<BR>\n" );
document.write( "b. Less than 50 minutes?<BR>\n" );
document.write( "c. Between 45 and 75 minutes?<BR>\n" );
document.write( "3- Bob takes an online IQ test and finds out that his IQ according to the test is 134. Assuming that the mean IQ is 100, the s=15, and the distribution of IQ scoes is normal, what proportion of the population would score higher than Bob? Lower than Bob? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248531 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=248531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1-the graduate selection committee wants to select the top 10% of applicants. On a standardized test with a mean of 500 and a standard diviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that test is normally distributed?<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Find the z-value with a right tail of 10%: invNorm(0.90) = 1.2816<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Then use x = zs+u to find the raw score (x).<BR>\n" );
document.write( "x = 1.2816*100+500 = 628.16<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "2- The average commute time via train from the chicago O'Hare Airport to downtown is 60 minutes with a s=15 minutes.Assume that the commute times are normally distributed. what proportion of commutes would be:<BR>\n" );
document.write( "a. Longer than 80 minutes?<BR>\n" );
document.write( "z(80) = (80-60)/15 = 4/3<BR>\n" );
document.write( "P(x> 80) = P(z> 4/3) = normalcdf(4/3,100) = 0.0912<BR>\n" );
document.write( "---------------------------------------------------------<BR>\n" );
document.write( "b. Less than 50 minutes?<BR>\n" );
document.write( "z(50) = (50-60)/15 = -2/3<BR>\n" );
document.write( "P(x< 50) = P(z< -2/3) = normalcdf(-100,-2/3) = 0.2525<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "c. Between 45 and 75 minutes?<BR>\n" );
document.write( "Same procedure.<BR>\n" );
document.write( "Can you do that?<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "3- Bob takes an online IQ test and finds out that his IQ according to the test is 134. Assuming that the mean IQ is 100, the s=15, and the distribution of IQ scoes is normal, what proportion of the population would score higher than Bob? Lower than Bob?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Find z-score of 134 = N.<BR>\n" );
document.write( "Find P(z >N)<BR>\n" );
document.write( "Find P(z < N)<BR>\n" );
document.write( "Can you do that?<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );