document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150310>Question 1150310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> percentage of orders filled correctly at burger king was 90.3% using binominal distribution what is the probability that 3 orders will be filled correctly out of 5 orders?<BR>\n" );
document.write( "what are the mean and standard deviation of the binominal distribution for the number of orders filed correctly out of 10 orders?<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 #771722 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=771722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "Question 1: what is the probability that 3 orders will be filled correctly out of 5 orders?\r<BR>\n" );
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document.write( "n = 5 is the sample size<BR>\n" );
document.write( "k = 3 is the number of successes (ie proper orders) we want of that sample size<BR>\n" );
document.write( "p = 0.903 is the probability of getting any single order correct\r<BR>\n" );
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document.write( "Compute the binomial coefficient using the nCr combination formula<BR>\n" );
document.write( "n C r = (n!)/(r!*(n-r)!)<BR>\n" );
document.write( "n C k = (n!)/(k!*(n-k)!)<BR>\n" );
document.write( "5 C 3 = (5!)/(3!*(5-3)!)<BR>\n" );
document.write( "5 C 3 = (5!)/(3!*2!)<BR>\n" );
document.write( "5 C 3 = (5*4*3!)/(3!*2!)<BR>\n" );
document.write( "5 C 3 = (5*4)/(2!)<BR>\n" );
document.write( "5 C 3 = (5*4)/(2*1)<BR>\n" );
document.write( "5 C 3 = 20/2<BR>\n" );
document.write( "5 C 3 = 10<BR>\n" );
document.write( "This value 10 can be found in Pascal's Triangle. Start with the row that has \"1,5,...\" at the beginning. Then count out k+1 = 3+1 = 4 spots over until you land on that second copy of \"10\". You count out k+1 spots instead of k spots because we start at k = 0 and not k = 1.\r<BR>\n" );
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document.write( "Now compute the binomial probability of getting exactly k = 3 orders correct<BR>\n" );
document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "P(X = 3) = (5 C 3)*(0.903)^3*(1-0.903)^(5-3)<BR>\n" );
document.write( "P(X = 3) = (5 C 3)*(0.903)^3*(0.097)^2<BR>\n" );
document.write( "P(X = 3) = (10)*(0.903)^3*(0.097)^2<BR>\n" );
document.write( "P(X = 3) = (10)*(0.736314327)*(0.009409)<BR>\n" );
document.write( "P(X = 3) = 0.06927981502743<BR>\n" );
document.write( "P(X = 3) = 0.0693<BR>\n" );
document.write( "P(X = 3) = 6.93%\r<BR>\n" );
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document.write( "The probability of getting three correct orders out of a sample of five is <font color=red>approximately 0.0693 which converts to 6.93%</font>\r<BR>\n" );
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document.write( "Question 2: what are the mean and standard deviation of the binomial distribution for the number of orders filed correctly out of 10 orders?\r<BR>\n" );
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document.write( "mu = mean<BR>\n" );
document.write( "sigma = standard deviation<BR>\n" );
document.write( "n = sample size = 10<BR>\n" );
document.write( "p = probability of getting any single order correct = 0.903\r<BR>\n" );
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document.write( "mu = n*p<BR>\n" );
document.write( "mu = 10*0.903<BR>\n" );
document.write( "mu = 9.03\r<BR>\n" );
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document.write( "sigma = sqrt(n*p*(1-p))<BR>\n" );
document.write( "sigma = sqrt(10*0.903*(1-0.903))<BR>\n" );
document.write( "sigma = 0.93590063575147<BR>\n" );
document.write( "sigma = 0.9359\r<BR>\n" );
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document.write( "For a sample of n = 10 orders, the binomial distribution for the number of correct orders will have <font color=red>a mean of 9.03</font> and <font color=red>a standard deviation of approximately 0.9359</font><BR>\n" );
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