document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=624406>Question 624406</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please show me specific detailed answers to these question i got wrong on my test. Thankyou. \r<BR>\n" );
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document.write( "An internal survey of a company showed that their staff needs to spend about 55 minutes from home to work every morning on average. It was also reported that 3% of the staff needs over two hours for the travel.\r<BR>\n" );
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document.write( "(i) If 50 staff is surveyed on a particular day, what is the probability that 5 will report the travel of over two hours?\r<BR>\n" );
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document.write( "(ii) If the company has 3000 staff, what is the expected number of staff who has the travel of over two hours?\r<BR>\n" );
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document.write( "(iii) If the company has 3000 staff, what are the variance and standard deviation of the number of staff who has the travel of over two hours?<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 #392770 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=392770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 55 minutes is the average.<BR>\n" );
document.write( "120 minutes is equal to 2 hours.<BR>\n" );
document.write( "3% take over 120 minutes.<BR>\n" );
document.write( "this looks like a binomial distribution type of problem.<BR>\n" );
document.write( "binomial distribution formula is:<BR>\n" );
document.write( "p(x) out of n = C(n,x) * p^x * q^(n-x)<BR>\n" );
document.write( "p(x) = probability of number of events that are successful<BR>\n" );
document.write( "n = total number<BR>\n" );
document.write( "p = probability that commute time will be greater than 120 minutes (success)<BR>\n" );
document.write( "q = probability that commute time will be less than or equal to 120 minutes (failure)<BR>\n" );
document.write( "c(n,x) is the combination formula for x events out of n = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "based on that:\r<BR>\n" );
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document.write( "i) If 50 staff are surveyed on a particular day, what is the probability that 5 will report the travel of over two hours?\r<BR>\n" );
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document.write( "p(5) out of 50 = C(50,5) * (.03)^5 * (.97)^45 = .013074229\r<BR>\n" );
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document.write( "(ii) If the company has 3000 staff, what is the expected number of staff who has the travel of over two hours?\r<BR>\n" );
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document.write( "expected number would be equal to n*p = 50 * .03 = 90\r<BR>\n" );
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document.write( "(iii) If the company has 3000 staff, what are the variance and standard deviation of the number of staff who has the travel of over two hours?\r<BR>\n" );
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document.write( "based on the binomial distribution formula:\r<BR>\n" );
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document.write( "variance is equal to n*p*q = 3000 * .03 * .97 = 87.3<BR>\n" );
document.write( "standard deviation is equal to square root of variance is equal to 9.343446901\r<BR>\n" );
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document.write( "a reference is here:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.stat.yale.edu/Courses/1997-98/101/binom.htm\" target = \"_blank\">http://www.stat.yale.edu/Courses/1997-98/101/binom.htm</a>\r<BR>\n" );
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document.write( "i think these are the answers you are looking for but i'm not totally sure.<BR>\n" );
document.write( "check them out and see if they agree with the answers you were supposed to have.\r<BR>\n" );
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