document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177793>Question 1177793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain electronics company produces a particular type of vacuum tube. It has been observed that, on the average, three tubes of 100 are defective. The company packs the tubes in boxes of 400. What is the probability that a certain box of 400 tubes will contain<BR>\n" );
document.write( "(a) r defective tubes ?<BR>\n" );
document.write( "(b) At least k defective tubes ?<BR>\n" );
document.write( "(c) At most one defective tube ?<BR>\n" );
document.write( "(d) Interpret your answers to (a), (b), and (c). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806901 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=806901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x+=+r%29=+highlight_green%28400Cr%29%28.03%5Er%29%28.97%29%5E%28400-r%29+ ALIGN=MIDDLE  ALT=\"P%28x+=+r%29=+highlight_green%28400Cr%29%28.03%5Er%29%28.97%29%5E%28400-r%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(b) P(x ≥ k) = 1 - P(x ≤ (k-1)) = 1 -  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28400C%28k-1%29%29%28.03%5E%28k-1%29%29%28.97%29%5E%28n-%28k-1%29%29+ ALIGN=MIDDLE  ALT=\"highlight_green%28400C%28k-1%29%29%28.03%5E%28k-1%29%29%28.97%29%5E%28n-%28k-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) P(x ≤ 1) = binomcdf(400, .03, 1) = .00006<BR>\n" );
document.write( "or<BR>\n" );
document.write( "  P(x=0) + P(x=1)<BR>\n" );
document.write( "(c)  Expected value .03*400 = 12<BR>\n" );
document.write( " in (a) as r approaches 12,  P gets larger.  In (b) P gets smaller<BR>\n" );
document.write( "in (c) the probability is small because x ≤ 1 is so much less that expected value of 12. </SPAN>\n" );
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