document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129435>Question 129435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that it is known that 5% of the items produced by a particular machine are defective in some way, and that we will choose a random sample of exactly 20 parts made by this machine.<BR>\n" );
document.write( "a.What is the expected number of defective items, out of the 20 we select?\r<BR>\n" );
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document.write( "b.What is the probability that exactly 1 of the 20 items is defective?\r<BR>\n" );
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document.write( "c. what is the probability that no more than 2 out of the 20 items selected are defective. \r<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 #94548 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=94548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that it is known that 5% of the items produced by a particular machine are defective in some way, and that we will choose a random sample of exactly 20 parts made by this machine.<BR>\n" );
document.write( "a.What is the expected number of defective items, out of the 20 we select?<BR>\n" );
document.write( "0.05*20 = 1<BR>\n" );
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document.write( "b.What is the probability that exactly 1 of the 20 items is defective? <BR>\n" );
document.write( "P(x=1) = 20C1(0.05)(0.95)^19 = 0.377...<BR>\n" );
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document.write( "c. what is the probability that no more than 2 out of the 20 items selected are defective.<BR>\n" );
document.write( "P(0<=x<=2) = binomcdf(20,0.05,2)= 0.9245...<BR>\n" );
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document.write( "Comment: The binomcdf is a function on a TI calculator.<BR>\n" );
document.write( "For example binomcdf(20,0,05,2) = 20C0(0.05)^0+0.95^20 + 20C1(0.05)(0.95)^19 <BR>\n" );
document.write( "+ 20C2(0.05)^2(0.95)^18 = 0.9245...<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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