document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187787>Question 1187787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the situation of Review Exercise 5.95.<BR>\n" );
document.write( "It has been determined that the sampling plan should<BR>\n" );
document.write( "be extensive enough that there is a high probability,<BR>\n" );
document.write( "say 0.9, that if as many as 2 defectives exist in the lot<BR>\n" );
document.write( "of 50 being sampled, at least 1 will be found in the<BR>\n" );
document.write( "sampling. With these restrictions, how many of the 50<BR>\n" );
document.write( "items should be sampled?\r<BR>\n" );
document.write( "\n" );
document.write( "Review Exercise 5.95.<BR>\n" );
document.write( "A production process outputs items in lots of 50.<BR>\n" );
document.write( "Sampling plans exist in which lots are pulled aside periodically and exposed to a certain type of inspection.<BR>\n" );
document.write( "It is usually assumed that the proportion defective is<BR>\n" );
document.write( "very small. It is important to the company that lots<BR>\n" );
document.write( "containing defectives be a rare event. The current inspection plan is to periodically sample randomly 10 out<BR>\n" );
document.write( "of the 50 items in a lot and, if none are defective, <BR>\n" );
document.write( "perform no intervention.<BR>\n" );
document.write( "(a) Suppose in a lot chosen at random, 2 out of 50 are<BR>\n" );
document.write( "defective. What is the probability that at least 1<BR>\n" );
document.write( "in the sample of 10 from the lot is defective?<BR>\n" );
document.write( "(b) From your answer to part (a), comment on the<BR>\n" );
document.write( "quality of this sampling plan.<BR>\n" );
document.write( "(c) What is the mean number of defects found out of<BR>\n" );
document.write( "10 items sampled?\r<BR>\n" );
document.write( "\n" );
document.write( "I tried:<BR>\n" );
document.write( "defective probability=0.2 (as many as 2 defective=>so I thought 1 and 2 defective) <BR>\n" );
document.write( "no defective=0.1<BR>\n" );
document.write( "p(defective)=2/50<BR>\n" );
document.write( "p(no defective)=48/50<BR>\n" );
document.write( "p(at least 1 defective)=1-p(no defective)=1-(48C10)/(50C10)=1-0.6367=0.3633\r<BR>\n" );
document.write( "\n" );
document.write( "and here I get confused.\r<BR>\n" );
document.write( "\n" );
document.write( "P(X<=2)=P(2)+P(1)+P(0)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850%21%2F48%212%21%29%2A0.9%5E2%2A0.1%5E48 ALIGN=MIDDLE  ALT=\"%2850%21%2F48%212%21%29%2A0.9%5E2%2A0.1%5E48\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850%21%2F49%211%21%29%2A0.9%5E1%2A0.1%5E49 ALIGN=MIDDLE  ALT=\"%2850%21%2F49%211%21%29%2A0.9%5E1%2A0.1%5E49\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850%21%2F50%210%21%29%2A0.9%5E0%2A0.1%5E50 ALIGN=MIDDLE  ALT=\"%2850%21%2F50%210%21%29%2A0.9%5E0%2A0.1%5E50\"   DISABLED_style= \"max-width:90%; height:auto;\" >=\r<BR>\n" );
document.write( "\n" );
document.write( "or is 0.9 supposed to be 2/50 and 0.1 supposed to be 48/50 ???\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you for your time :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818934 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52805)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Toooooooooooooo  long post to read . . . \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The rule is simple.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Math problem can not be longer than 5 lines of standard text - otherwise, nobody and never will read it . . . \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );