document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201749>Question 1201749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 15 flights are randomly selected, and the number of on-time flights is recorded.\r<BR>\n" );
document.write( "\n" );
document.write( "Note: Write your answer rounded to four decimal places.\r<BR>\n" );
document.write( "\n" );
document.write( "(a) Find the probability that exactly 11 flights are on time. <BR>\n" );
document.write( "0.1136\r<BR>\n" );
document.write( "\n" );
document.write( "(b) Find the probability that fewer than 11 flights are on time. \r<BR>\n" );
document.write( "\n" );
document.write( "(c) Find the probability that at least 11 flights are on time. \r<BR>\n" );
document.write( "\n" );
document.write( "(d) Find the probability that between 9 and 11 flights, inclusive, are on time. \r<BR>\n" );
document.write( "\n" );
document.write( "(e) Compute the mean and standard deviation of the random variable X, the number of on-time flights in 15 trials of the probability experiment.\r<BR>\n" );
document.write( "\n" );
document.write( "Mean <BR>\n" );
document.write( " , Standard deviation <BR>\n" );
document.write( " . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836251 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52800)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "According to flightstats.com, American Airlines flights from Dallas to Chicago <BR>\n" );
document.write( "are on time 80% of the time. Suppose 15 flights are randomly selected, <BR>\n" );
document.write( "and the number of on-time flights is recorded.<BR>\n" );
document.write( "Note: Write your answer rounded to four decimal places.<BR>\n" );
document.write( "(a) Find the probability that exactly 11 flights are on time.<BR>\n" );
document.write( "0.1136<BR>\n" );
document.write( "(b) Find the probability that fewer than 11 flights are on time.<BR>\n" );
document.write( "(c) Find the probability that at least 11 flights are on time.<BR>\n" );
document.write( "(d) Find the probability that between 9 and 11 flights, inclusive, are on time.<BR>\n" );
document.write( "(e) Compute the mean and standard deviation of the random variable X, the number of on-time flights in 15 trials of the probability experiment.<BR>\n" );
document.write( "Mean<BR>\n" );
document.write( "Standard deviation<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is a typical binomial distribution probability problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Go to web-site https://stattrek.com/online-calculator/binomial.aspx\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and use free of charge online calculator there, specially developed for such problems.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The number of trials is n= 15;  the probability p of each success individual trial is 0.8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a) p = P(n=15;  k=11; p=0.8) = 0.1876.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b) p = P(n=15; k<11; p=0.8) = 0.16424.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c) p = P(n=15; k>=11; p=0.8) = 0.83576.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(d) p = P(n=15; 9<= k <=11; p=0.8) = P(n=15; k<=11; p=0.8) - P(n=15; k<9; p=0.8) = 0.35184 - 0.01806 = 0.33378.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(e) Mean = n*p = 15*0.8 = 1.2\r\n" );
document.write( "\r\n" );
document.write( "    SD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%2Ap%2A%281-p%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28n%2Ap%2A%281-p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815%2A0.8%2A%281-0.8%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2815%2A0.8%2A%281-0.8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.5492  (rounded).\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved, with all necessary explanations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To see a variety similar solved problems, &nbsp;look into the lessons\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson>How to calculate Binomial probabilities with Technology (using MS Excel)</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson>Solving problems on Binomial distribution with Technology (using MS Excel)</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson>Solving problems on Binomial distribution with Technology (using online solver)</A> \r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "After reading these lessons, &nbsp;you will be able to solve such problems on your own, \r<BR>\n" );
document.write( "\n" );
document.write( "which is your &nbsp;PRIMARY &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );