document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118388>Question 1118388</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The mean salary offered to students who are graduating from Coastal State University this year is $24,215, with a standard deviation of $3678. A random sample of 85 Coastal State students graduating this year has been selected. What is the probability that the mean salary offer for these 85 students is $24,500 or less?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733733 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the population mean is 24215<BR>\n" );
document.write( "the population standard deviation is 3678.\r<BR>\n" );
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document.write( "the sample size is 85.<BR>\n" );
document.write( "the standard deviation of the distribution of sample means, called the standard error, from samples whose size is 85 is equal to 3678 / sqrt(85) = 398.9351119.\r<BR>\n" );
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document.write( "the z-score for a sample mean of 24500 or less from this population, with a sample size of 85, is z = (24500 - 24215) / 398.9351119 = .7143732313.\r<BR>\n" );
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document.write( "the area under the normal distribution curve to the left of this z-score is equal to  .7625107243.\r<BR>\n" );
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document.write( "that means the probability that you would get a sample of size 85 whose mean is 24500 or less is .7625107243, or approximately 76.25%.\r<BR>\n" );
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document.write( "this can be seen visually in the following graph.\r<BR>\n" );
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