document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130766>Question 130766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this homework question ASAP. It is not from textbook. it is for the probability and statistics class. <BR>\n" );
document.write( "can i solve this question this way:<BR>\n" );
document.write( "P(X = 3) = since each component has probability of functioning as 0.9. the probability of not functioning is 1-0.9 = 0.1. <BR>\n" );
document.write( "so 3 system out of 5 will have = (0.9)(0.9)(0.9) = 0.729 ?  is this correct for part a?<BR>\n" );
document.write( "b. atleast 3 out of 5 will function. is this correct?<BR>\n" );
document.write( "c. (3)(0.9) = 2.7?\r<BR>\n" );
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document.write( "question:   A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. Assume the components function independently of one another.\r<BR>\n" );
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document.write( "1). In 3 out 5 system, each component has probability 0.9 of functioning. What is the probability that the system will function?\r<BR>\n" );
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document.write( "2). Based on the information given in 1), what is the expected number of components that function.\r<BR>\n" );
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document.write( "3). In a 3 out n system, in which each component has probability 0.9 of functioning, what is the smallest values of n needed so that the probability that the system functions is at least 0.90?\r<BR>\n" );
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document.write( "I really appreciate the help with homeworks that you guys provide.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95480 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=95480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(X = 3) = since each component has probability of functioning as 0.9. the probability of not functioning is 1-0.9 = 0.1. <BR>\n" );
document.write( "so 3 system out of 5 will have = (0.9)(0.9)(0.9) = 0.729 ? is this correct for part a?<BR>\n" );
document.write( "P(3 successes in 5 trials) = 5C3(0.9)^3(0.1)^2 = 0.0729<BR>\n" );
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document.write( "b. at least 3 out of 5 will function.<BR>\n" );
document.write( "P(at least 3 out of 5) = 1 - binomcdf(5,0.9,2) = 0.99144<BR>\n" );
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document.write( "c. (3)(0.9) = 2.7?<BR>\n" );
document.write( "I don't understand your \"c\" question.<BR>\n" );
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document.write( "question: A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. Assume the components function independently of one another. <BR>\n" );
document.write( "1). In 3 out 5 system, each component has probability 0.9 of functioning. What is the probability that the system will function? <BR>\n" );
document.write( "Prob = 1-binomcdf(5,0.9,2) = \r<BR>\n" );
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document.write( "2). Based on the information given in 1), what is the expected number of components that function.<BR>\n" );
document.write( "Expected value is the mean which is np for binomial distributions.<BR>\n" );
document.write( "Expected value = 5*0.9 = 4.5<BR>\n" );
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document.write( "3). In a 3 out n system, in which each component has probability 0.9 of functioning, what is the smallest values of n needed so that the probability that the system functions is at least 0.90?<BR>\n" );
document.write( "We know 3 out of 5 is 0.99<BR>\n" );
document.write( "Try 3 out of 4: 1-binomcdf(4,0.9,2)= 0.9477<BR>\n" );
document.write( "Try 3 out of 3: 1-binomcdf(3,0.9,2)= 0.729<BR>\n" );
document.write( "Looks like n=4 will do the job.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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