document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=921812>Question 921812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am desperate! please help!\r<BR>\n" );
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document.write( "The average salary for graduates entering the actuarial field is $40,000 ( ). If the salaries are normally distributed with a standard deviation of $5000 (&#963; = 5000), find the probability that:<BR>\n" );
document.write( "a.	An individual graduate (n = 1) will have a salary over $45,000: P(X > 45,000).<BR>\n" );
document.write( "b.	A group of nine graduates (n = 9) will have an average over $45,000: P( )<BR>\n" );
document.write( "c.	A group of nine graduates (n = 50) will have an average over $45,000: P( )<BR>\n" );
document.write( "d.	A group of nine graduates (n = 125) will have an average over $45,000: P( )<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559236 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=559236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For normal distributions we use z-value to determine probabilities (Pr),<BR>\n" );
document.write( "we are given that the mean is 40000 and standard deviation is 5000<BR>\n" );
document.write( "a) Pr(X>45000) = 1 - Pr(X<45000)<BR>\n" );
document.write( "calculate the z-value = (45000 - 40000) / 5000 = 1, consult z-tables<BR>\n" );
document.write( "Pr(X<45000) = 0.8413<BR>\n" );
document.write( "Pr(X>45000) = 1 - 0.8413 = 0.1587<BR>\n" );
document.write( "b) with a sample space of 9 students, we calculate a new standard deviation<BR>\n" );
document.write( "sample standard deviation = standard deviation / square root (n)<BR>\n" );
document.write( "sample standard deviation = 5000 / square root (9) = 1666.666666667<BR>\n" );
document.write( "Pr(X>45000) = 1 - Pr(X<45000)<BR>\n" );
document.write( "calculate the z-value = (45000 - 40000) / 1666.666666667 = 3 , consult z-tables<BR>\n" );
document.write( "Pr(X<45000) = 0.9987<BR>\n" );
document.write( "Pr(X>45000) = 1 - 0.9987 = 0.0013<BR>\n" );
document.write( "c)n = 50, for n > 40 use the population standard deviation<BR>\n" );
document.write( "sample standard deviation = 5000<BR>\n" );
document.write( "calculate the z-value = (45000 - 40000) / 5000 = 1 , consult z-tables<BR>\n" );
document.write( "Pr(X>45000) = 1 - 0.8413 = 0.1587<BR>\n" );
document.write( "d) n = 125, for n > 40 use the population standard deviation<BR>\n" );
document.write( "sample standard deviation = 5000<BR>\n" );
document.write( "calculate the z-value = (45000 - 40000) / 5000 = 1 , consult z-tables<BR>\n" );
document.write( "Pr(X>45000) = 1 - 0.8413 = 0.1587<BR>\n" );
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