document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163901>Question 1163901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Aproduction process outputs items in lots of 50. Sampling plans exist in which lots are pulled aside periodically and exposed to a certain type of inspection. It is usually assumed that the proportion defective is very small. It is important to the company that lots containing defectives be a rare event. The current inspection plan is to periodically sample randomly 10 out of the 50 items in a lot and, if none are defective, to perform no intervention. (a) Suppose in a lot chosen at random, 2 out of 50 are defective. What is the probability that at least 1 in the sample of 10 from the lot is defective? (b) From your answer to part (a), comment on the quality of this sampling plan. (c) What is the mean number of defects found out of 10 items sampled? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788217 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If 2 out of 50 are defective,<BR>\n" );
document.write( "probability 0 are defective in a sample of 10 is <BR>\n" );
document.write( "10C0*40C2/50C2<BR>\n" );
document.write( "=0.6367<BR>\n" );
document.write( "Therefore, the probability at least 1 is defective is the complement or 1-0.6367 or 0.3633.\r<BR>\n" );
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document.write( "With 4% defective overall, there is a 1/3 chance sampling 10 will show 1 defective. What is the quality of the plan?  I think a better question is  what are the consequences of letting a defective product through?  The sampling effectiveness at finding 1 defect in 10 sampled is about 1/3, given a 4% overall defect rate. A lot of samples will show defects given this percentage.\r<BR>\n" );
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document.write( "What is the probability of finding 1 defective?<BR>\n" );
document.write( "10C1*40C1/50C2=0.3265<BR>\n" );
document.write( "and 2 defective would be 0.0408<BR>\n" );
document.write( "the mean or Expected Value is p(x)*x or 0.3265*1+0.0408*2=0.4081 defective out of 10 items sampled.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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