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 #667054 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We use the binary probability distribution<BR>\n" );
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document.write( "The probability of non-defective items is 1 - 0.25 = 0.75<BR>\n" );
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document.write( "Probability(k items are non-defective) = nCk * p^k * q^(n-k), where n is number of items produced, k = number of non-defective items, p = probability of non-defective items, q = 1-p, nCk of the combination of n items taken k at a time<BR>\n" );
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document.write( "a) Probability(k items are non-defective) = nCk * (0.75)^k * (0.25)^(n-k)<BR>\n" );
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document.write( "b) Probability(at least 50 items are produced out of 100) is the summation of<BR>\n" );
document.write( "the probabilities for 50, 51, 52, ..., 100<BR>\n" );
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document.write( "Probability(at least 50 items are produced out of 100) = 0.999999 </SPAN>\n" );
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