document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051583>Question 1051583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this problem:\r<BR>\n" );
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document.write( "In a certain production process, 25% of the items produced are found defective. It therefore requires through inspection of all the items produced before packing them for sale.\r<BR>\n" );
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document.write( "a) Develop a probability density function for the number of non-defective items in a day's production of n items.\r<BR>\n" );
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document.write( "b) Using your answer to a), determine the probability of getting at least 50 good items if 100 items are produced.<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 #667057 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=667057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)<BR>\n" );
document.write( "p(def) = .25, p(not def) = .75<BR>\n" );
document.write( " probability density function for the number of non-defective items in a day's production of n items. <BR>\n" );
document.write( "Let x represent the number of non-defective itemsin a day's production of n items <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+%28x%29=+highlight_green%28nCx%29%28.75%5Ex%29%28.25%29%5E%28n-x%29+ ALIGN=MIDDLE  ALT=\"P+%28x%29=+highlight_green%28nCx%29%28.75%5Ex%29%28.25%29%5E%28n-x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "p = .75, n = 100<BR>\n" );
document.write( "P (x>= 50)  Commulative Probability\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+%28x%3E=+50%29+=+1+-+P+%28x%3C+49%29+=+1+-+sum%28+highlight_green%28100Cx%29%28.75%5Ex%29%28.25%29%5E%28100-x%29%2C+x=0%2C+49+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P (x>= 50) = 1 - binomcdf(100,.75,49) = 1 - .000002 = .999998<BR>\n" );
document.write( "P (x>= 50) basically a sure thing. \r<BR>\n" );
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