document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=260100>Question 260100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble understanding this. Can someone please help me?\r<BR>\n" );
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document.write( "The probabilities that a batch of 4 computers will contain 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, and 0.001 respectively.\r<BR>\n" );
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document.write( "a.  Set up a probability distribution to describe this situation.<BR>\n" );
document.write( "b.  Based on these probabilities how many defective computers would you expect to find in this batch?  (This would be the mean of the distribution.)<BR>\n" );
document.write( "c.  How much would this value reasonably be expected to fluctuate?  (This is the standard deviation.)<BR>\n" );
document.write( "d.  What’s the probability of finding at most 2 defective computers in this batch?  <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 #191550 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=191550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probabilities that a batch of 4 computers will contain 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, and 0.001 respectively. <BR>\n" );
document.write( "a. Set up a probability distribution to describe this situation.<BR>\n" );
document.write( "The only number missing is zero.<BR>\n" );
document.write( "Add the probabilities you are given and subtract that sum from 1 to<BR>\n" );
document.write( "get the probability of zero computers being defective.<BR>\n" );
document.write( "I get: 1 - 0.9961 = 0.0039<BR>\n" );
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document.write( "Now write the ordered pairs:<BR>\n" );
document.write( "(0,0.0039),(1,0.6274),etc<BR>\n" );
document.write( "That is the probability distribution<BR>\n" );
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document.write( "b. Based on these probabilities how many defective computers would you expect<BR>\n" );
document.write( "E(x) = 0*0.0039 + 1*0.6274 + 2*0.3102 + etc<BR>\n" );
document.write( "to find in this batch? (This would be the mean of the distribution.)<BR>\n" );
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document.write( "c. How much would this value reasonably be expected to fluctuate? (This is the standard deviation.)<BR>\n" );
document.write( "That is a messy problem unless you have a calculator or software that<BR>\n" );
document.write( "will work it for you.<BR>\n" );
document.write( "I get std = 0.6108.. using a TI calculator.<BR>\n" );
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document.write( "d. What’s the probability of finding at most 2 defective computers in this batch? <BR>\n" );
document.write( "P(2<= x <=4) = 1 - [P(x=0 + P(x=1) = 1- [0.0039+0.6274] = 0.3687<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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