document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965005>Question 965005</A>: <I><SPAN STYLE=\"word-break: break-all;\">  An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of 140 American college students found 42 with brown eyes.<BR>\n" );
document.write( "(a). Give the numerical value of the sample proportion \hat{p}. <BR>\n" );
document.write( "\hat{p} =\r<BR>\n" );
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document.write( "(b). Assuming that 45% of the population have brown eyes, determine the mean and standard deviation of the distribution of sample proportions for samples of size n = 140.\r<BR>\n" );
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document.write( "The mean is \r<BR>\n" );
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document.write( "The standard deviation is  \r<BR>\n" );
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document.write( "(c). What is the probability that in a random sample of 140 Americans, more than 47.2 % have brown eyes?\r<BR>\n" );
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document.write( "The probability is  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589802 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=589802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) ^p = 42 / 140 = 0.30<BR>\n" );
document.write( "b) P = .45 and Q = .55, then<BR>\n" );
document.write( "The mean = P = .45<BR>\n" );
document.write( "Standard Deviation = sqrt(PQ/n) = sqrt((.45*.55) / 140) = 0.042045893 approx 0.04<BR>\n" );
document.write( "c) z-score = (X - mean) / std dev = (0.472 - 0.45) / 0.04 = 0.55<BR>\n" );
document.write( "consult the z-tables for the probability associated with z-score = 0.55<BR>\n" );
document.write( "The probability (X < 0.472) = 0.7088 approx .71<BR>\n" );
document.write( "now we want the probability (X > 0.472) which is equal to<BR>\n" );
document.write( "1 - 0.71 = 0.29<BR>\n" );
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