document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081808>Question 1081808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am having a lot of trouble with Normal Distribution. I do online school and the lessons don't do a very good job of explaining exactly how to solve these problems. My teacher said that all of the following problems were answered incorrectly. Any help is greatly appreciated!!<BR>\n" );
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document.write( "Consider this scenario for questions 5 - 8. <BR>\n" );
document.write( "A standardized test was given to a set of high school juniors and the distribution of the data is bell shaped. The mean score is 800 and the standard deviation is 120. \r<BR>\n" );
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document.write( "5. Between which two scores did 95% of the students score? \r<BR>\n" );
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document.write( "6. To qualify for a special summer camp for accelerated students, a student must score within the top 16% of all scores on the test. What score must a student make to qualify for summer camp? <BR>\n" );
document.write( "z = +1.96 <BR>\n" );
document.write( "x = &#956;+&#963;*z <BR>\n" );
document.write( "x = 74+8(1.96) <BR>\n" );
document.write( "x = 89.68 <BR>\n" );
document.write( "90 <BR>\n" );
document.write( "7. What score is 1/2 standard deviation above the mean? <BR>\n" );
document.write( "z = 1/2 <BR>\n" );
document.write( "score = 800 + (1/2)120 = 860 <BR>\n" );
document.write( "8. A student scores 900 on the test. How many more points did the student need to qualify for summer camp? <BR>\n" );
document.write( "5/ <BR>\n" );
document.write( "(800 - 240 , 800+240) <BR>\n" );
document.write( "6/ <BR>\n" );
document.write( "920 <BR>\n" );
document.write( "7/ <BR>\n" );
document.write( "800-240 <BR>\n" );
document.write( "560 <BR>\n" );
document.write( "Consider the following scenario for questions 9-12. <BR>\n" );
document.write( "On the average, members at a local fitness center work out for 90 minutes with a standard deviation of 15 minutes. The distribution is normal. <BR>\n" );
document.write( "9. What percentage of the fitness club members work out for 45 minutes or less? <BR>\n" );
document.write( "z(45) = (45-90)/15 = -45/15 = -3 <BR>\n" );
document.write( "P(x <= 45) = P(z <= -3) = (-100,-3) <BR>\n" );
document.write( "0.3% \r<BR>\n" );
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document.write( "10. What percentage of the fitness club members work out for 2 hours and 15 minutes or more? <BR>\n" );
document.write( "z = (135 - 90)/15 <BR>\n" );
document.write( "3%<BR>\n" );
document.write( "11. 68% of the fitness club members work out between which two time intervals? <BR>\n" );
document.write( "P(Z < z) = 0.84 <BR>\n" );
document.write( "0.5+0.34 <BR>\n" );
document.write( "68% within 1 sd <BR>\n" );
document.write( "between 75 and 105 minutes \r<BR>\n" );
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document.write( "12. We can say that 99.7% of the fitness club members work out for no more than 135 minutes. <BR>\n" );
document.write( "(Mean - 3 × std) and (Mean + 3 × std) <BR>\n" );
document.write( "(90 - 3 × 15) and (90 + 3 × 15) <BR>\n" );
document.write( "45 – 135 <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695854 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean 800 sd 120<BR>\n" );
document.write( "the middle 95% is from z.025 to z.975 which is +/- 1.96<BR>\n" );
document.write( "z=(x-mean)/sd<BR>\n" );
document.write( "1.96=(x-800)/120<BR>\n" );
document.write( "235.2=x-800<BR>\n" );
document.write( "x=1035.2 at top end and 664.8 at bottom end<BR>\n" );
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document.write( "84th percentile from table is z=+0.95<BR>\n" );
document.write( "0.95=(x-mean)/120<BR>\n" );
document.write( "114=x-800<BR>\n" );
document.write( "914= the critical value<BR>\n" );
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document.write( "Half sd above the mean has a score of 860; 900 is 14 points shy of qualifying.<BR>\n" );
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document.write( "9 is mostly correct, except 0.3% is double what it should be.  The result is 0.0013 or .13%<BR>\n" );
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document.write( "10 is the same at the opposite end, the per cent more than+3 sd, which is not the same as the per cent more than +/- 3 sd.<BR>\n" );
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document.write( "11 is correct.<BR>\n" );
document.write( "12. We can say that 99.87% work out for no more than 135 minutes. </SPAN>\n" );
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