document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192872>Question 1192872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean = 548.4 and standard deviation = 28.1 .<BR>\n" );
document.write( "(a) What is the probability that a single student randomly chosen from all those taking the test scores 553 or higher?<BR>\n" );
document.write( "ANSWER: \r<BR>\n" );
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document.write( "For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.\r<BR>\n" );
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document.write( "(b) What are the mean and standard deviation of the sample mean score x <BR>\n" );
document.write( ", of 35 students?<BR>\n" );
document.write( "The mean of the sampling distribution for x<BR>\n" );
document.write( " is: \r<BR>\n" );
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document.write( "The standard deviation of the sampling distribution for <BR>\n" );
document.write( " is: \r<BR>\n" );
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document.write( "(c) What z-score corresponds to the mean score x<BR>\n" );
document.write( " of 553?<BR>\n" );
document.write( "ANSWER: \r<BR>\n" );
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document.write( "(d) What is the probability that the mean score x<BR>\n" );
document.write( " of these students is 553 or higher?<BR>\n" );
document.write( "ANSWER: \r<BR>\n" );
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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 #824922 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=824922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "z>(553-548.4)/28.1=0.1637<BR>\n" );
document.write( "probability z > 0.1637 is 0.4350<BR>\n" );
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document.write( "for 35 students, the mean of the sampling distribution is 548.4, no change.<BR>\n" );
document.write( "the sd is original sd/sqrt(n)=4.75<BR>\n" );
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document.write( "z now is 4.6/4.75=0.97<BR>\n" );
document.write( "the probability now is 0.1664 </SPAN>\n" );
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