document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168751>Question 1168751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the problem.\r<BR>\n" );
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document.write( "The scores on a certain test are normally distributed with a mean score of 66 and a standard deviation of 3. What is the probability that a sample of 90 students will have a mean score of at least 66.3162? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793368 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=793368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given info:<BR>\n" );
document.write( "xbar = sample mean = 66.3162<BR>\n" );
document.write( "mu = population mean = 66<BR>\n" );
document.write( "sigma = population standard deviation = 3<BR>\n" );
document.write( "n = sample size = 90<BR>\n" );
document.write( "The goal is to calculate P(xbar > 66.3162)\r<BR>\n" );
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document.write( "Calculate the standard error (SE)<BR>\n" );
document.write( "SE = sigma/sqrt(n)<BR>\n" );
document.write( "SE = 3/sqrt(90)<BR>\n" );
document.write( "SE = 0.31622776601683\r<BR>\n" );
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document.write( "Use that to find the z score<BR>\n" );
document.write( "z = (xbar - mu)/SE<BR>\n" );
document.write( "z = (66.3162-66)/0.31622776601683<BR>\n" );
document.write( "z = 0.9999121961453<BR>\n" );
document.write( "z = 1.00\r<BR>\n" );
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document.write( "The problem of finding P(xbar > 66.3162) is approximately the same as wanting to find P(Z > 1.00)\r<BR>\n" );
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document.write( "At this point, you'll need a table or calculator. <BR>\n" );
document.write( "If you go with a table, then you can use a table in the back of your book or you can use a free online resource like this<BR>\n" );
document.write( "http://www.z-table.com/\r<BR>\n" );
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document.write( "That website shows a Z table<BR>\n" );
document.write( "In that table, we see that P(Z < 1.00) = 0.8413<BR>\n" );
document.write( "Look in the row that starts with 1.0 and the column that starts with 0 to find the value 0.8413<BR>\n" );
document.write( "This represents the area under the curve to the left of the z value z = 1.00\r<BR>\n" );
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document.write( "Subtract the value from 1 to get the area under the curve to the right of the z value in question<BR>\n" );
document.write( "1-0.8413 = 0.1587\r<BR>\n" );
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document.write( "The final answer is 0.1587<BR>\n" );
document.write( "This means there's roughly a 15.87% chance that xbar is larger than 66.3162<BR>\n" );
document.write( "Use a calculator to get better accuracy.\r<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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