document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162116>Question 1162116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the mean test score of 50 students in a statistics class is 80 with a standard deviation of 7. if the test scores known to be normally distributed, calculate the following.<BR>\n" );
document.write( "1. what proportion of the students who scored between 80 and 90?<BR>\n" );
document.write( "2. what percentage of the students who scored from 60 to 80?<BR>\n" );
document.write( "3. what is the probability of the students who scored between 70 and 85?<BR>\n" );
document.write( "4. how many students have scored between 85 and 96?<BR>\n" );
document.write( "5. how many students obtained a score range from 68 to 75?<BR>\n" );
document.write( "6. howmany students who scored greater than 93?<BR>\n" );
document.write( "7. How many of the students scored less than 65?<BR>\n" );
document.write( "8.find the percentage of the students who scored less than 90?<BR>\n" );
document.write( "9.if 30% of the students fail, what is the passing score?<BR>\n" );
document.write( "10. Find the range of score that covers the central 78.88% of the students? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786030 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=786030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd <BR>\n" );
document.write( "=(80-80)/7=0<BR>\n" );
document.write( "=(90-80)/7=1.43<BR>\n" );
document.write( "want z between 0 and 1.43, which is 0.4236<BR>\n" );
document.write( "OR, and you can do this with all, go to 2nd VARS 2 Normalcdf (80,90,80,7). put in the two limits followed by the mean and the sd. ENTER. \r<BR>\n" );
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document.write( "so for 4. put in for normalcdf (85,96,80,7)ENTER  0.2264 probability.\r<BR>\n" );
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document.write( "for 6, put in a large number like 1000. normal cdf (93,1000,80,7)\r<BR>\n" );
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document.write( "for 9. use 2ndENTER 2 invnorm (0.30,80,7) ENTER. Get 76.3<BR>\n" );
document.write( "z(0.30)=-0.5244<BR>\n" );
document.write( "z=(x-mean)/sd<BR>\n" );
document.write( "-0.524*7=x-mean<BR>\n" );
document.write( "x=80-3.67=76.3\r<BR>\n" );
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document.write( "there is 21.12% remaining, (100-78.88) and half of that is 10.56%<BR>\n" );
document.write( "inv norm (0.1056,50,7)=41.25<BR>\n" );
document.write( "that is 8.75 below the mean. The normal function is symmetrical, so the other side will be 8.75 above the mean, and that would be 58.75.\r<BR>\n" );
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document.write( "Check with normal cdf (41.25, 58.75, 50, 7)=0.7887, which is off by rounding error. Use 3 decimal places. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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