document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464471>Question 464471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A mandatory high school test is normally distributed with mean 400 and standard deviation 73.<BR>\n" );
document.write( "A. Find the probability that a randomly chosen student has a score better than 500?<BR>\n" );
document.write( "B. Find the probability that a randomly chosen student has a score between 350 and 550?<BR>\n" );
document.write( "C. The top 3% of all students are eligible for a scholarship. What is the minimu score needed to be eligible for the scholarship?<BR>\n" );
document.write( "Could you please show the exact steps for solving these questions?<BR>\n" );
document.write( "Thanks in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318187 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)<BR>\n" );
document.write( "z=(500-400)/73=1.37<BR>\n" );
document.write( "The area below 1.37 under the normal curve is .915 the probability that a randomly chosen student has a score better than 500.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b)<BR>\n" );
document.write( "z=(550-400)/73=2.05<BR>\n" );
document.write( "z=(350-400)/73=-.685<BR>\n" );
document.write( "The area between 2.05 and -.685 under the normal curve is .733  the probability that a randomly chosen student has a score between 350 and 550.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c)<BR>\n" );
document.write( "The area under the normal curve of .03 on the right is above 1.88<BR>\n" );
document.write( "(x-400)/73=1.88<BR>\n" );
document.write( "x-400=137.24<BR>\n" );
document.write( "x=538 the minimum score needed to be eligible for the scholarship (537 is acceptable).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );