document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086635>Question 1086635</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The United Package Service has a policy that states if a package is delivered late they will reimburse their shipping fees.  They deliver packages late only 5% of the time.  If a delivery person has 7 deliveries one day, what is the probability that at most 1 package is arriving late?  Round your answer to the nearest ten-thousandth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700883 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( "The United Package Service has a policy that states if a package is delivered late they will reimburse their shipping fees.  They deliver packages late only 5% of the time.  If a delivery person has 7 deliveries one day, what is the probability that at most 1 package is arriving late?  Round your answer to the nearest ten-thousandth.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "To determine if the problem can be modelled using the binomial distribution, we need to examine the following criteria:<BR>\n" );
document.write( "1. Bernoulli trials, i.e. exactly two possible outcomes (Late or not late)<BR>\n" );
document.write( "2. Number of trials is known before experiment, i.e. independent of outcomes (7 per day)<BR>\n" );
document.write( "3. All trials are independent of each other (assumed true)<BR>\n" );
document.write( "4. Probability of success is known, and remain constant throughout trials (p=5%=0.05)<BR>\n" );
document.write( "Since all the criteria are satisfied, binomial distribution will be used.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The probability of x successes out of N trials each with probability of success p is given by<BR>\n" );
document.write( "P(x)=C(N,x)(p^x)(1-p)^(N-x)<BR>\n" );
document.write( "where <BR>\n" );
document.write( "C(N,x) is number of combinations of selecting x objects out of N.\r<BR>\n" );
document.write( "\n" );
document.write( "p=0.05<BR>\n" );
document.write( "n=7<BR>\n" );
document.write( "x=0 and x=1<BR>\n" );
document.write( "P(\"at most one package late\") =P(0)+P(1)<BR>\n" );
document.write( "=C(7,0)*0.05^0*(1-0.05)^7+C(7,1)*0.05^1*(1-0.05)^6<BR>\n" );
document.write( "=0.6983+0.2573<BR>\n" );
document.write( "=0.9556<BR>\n" );
document.write( "Probability of at most one delivery late is 0.9556. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );