document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=859938>Question 859938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> About 4% of the scientists in the National Academy of Sciences believe in PSI (parapsychology such as psychokinesis, telepathy, and astral projection). At a convention 107 members show up. Let X be the number of scientists at the convention who believe in PSI. You may assume for the following questions that X is binomially distributed with parameters n=107 and p=0.04.\r<BR>\n" );
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document.write( "(a) How many scientists at the convention do you expect do believe in PSI? Answer\r<BR>\n" );
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document.write( "(b) What are the chances that none of the scientists at the convention believes in PSI? Answer\r<BR>\n" );
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document.write( "(c) What are the chances that at least 4 scientists at the convention believe in PSI? Answer\r<BR>\n" );
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document.write( "(d) What is the standard deviation of X </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #518077 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=518077\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> About 4% of the scientists in the National Academy of Sciences believe in PSI (parapsychology such as psychokinesis, telepathy, and astral projection). At a convention 107 members show up. Let X be the number of scientists at the convention who believe in PSI. You may assume for the following questions that X is binomially distributed with parameters n=107 and p=0.04. <BR>\n" );
document.write( "(a) How many scientists at the convention do you expect to believe in PSI? Answer:: np = 107*0.04 = 4.28<BR>\n" );
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document.write( "(b) What are the chances that none of the scientists at the convention believes in PSI? Answer P(x = 0) = 0.96^107 = 0.0127<BR>\n" );
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document.write( "(c) What are the chances that at least 4 scientists at the convention believe in PSI? Answer:: P(4<= x <=107) = 1-P(0<=x<=3) <BR>\n" );
document.write( "= 1-binomcdf(107,0.04,3) = 0.6240<BR>\n" );
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document.write( "(d) What is the standard deviation of X<BR>\n" );
document.write( "std = sqrt(npq) = sqrt(107*0.04*0.96) = 2.0270<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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