document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=623540>Question 623540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ACCORDING TO A RECENT STUDY 38% OF ALL WOMEN WILL SUFFER A HIP FRACTURE BECAUSE OF OSTEOPOROSIS BY THE AGE OF 85. IF SIX WOMEN AGED 85 ARE RANDOMLY SELECTED WHAT IS THE PROBABILITY THAT FEWER THAN TWO OF THEM WILL SUFFER (OR HAVE SUFFERED) A HIP FRACTURE DUE TO OSTEOPOROSIS<BR>\n" );
document.write( "please show how you obtained answer without The binomcdf( Command as that will not help me Thanx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #392169 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=392169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the woman is 85, then the probability of having a hip fracture is .38<BR>\n" );
document.write( "this means that the probability of not having a hip fracture is 1 - .38 = .62<BR>\n" );
document.write( "p(having) + p(not having) = .38 + .62 = 1.0 as it should.<BR>\n" );
document.write( "since this is a binomial distribution, you have to use the binomial distribution formula to get the answers.<BR>\n" );
document.write( "that formula is:<BR>\n" );
document.write( "p(x) = C(n,x) * p^x * q^(n-x)<BR>\n" );
document.write( "n is equal 6 because you're dealing with 6 women.<BR>\n" );
document.write( "x is equal to the number of hip injuries among the 6 women.<BR>\n" );
document.write( "p is equal to the probability of having a hip injury.<BR>\n" );
document.write( "q is equal to the probability of not having a hip injury.<BR>\n" );
document.write( "C(n,x) is the combination formula of n! / (x! * (n-x)!)<BR>\n" );
document.write( "as an example:<BR>\n" );
document.write( "when x is equal to 0, the formula tells you that the probability is:<BR>\n" );
document.write( "p(0) = C(6,0) * .38^0 * .62^6<BR>\n" );
document.write( "when x is equal to 1, the formula tells you that the probability is:<BR>\n" );
document.write( "p(1) = C(6,1) * .38^1 * .62^5<BR>\n" );
document.write( "when x is equal to 2, the formula tells you that the probability is:<BR>\n" );
document.write( "p(2) = C(6,2) * .38^2 * .62^4<BR>\n" );
document.write( "etc down to x is equal to 6, the formula tells you that the probability is:<BR>\n" );
document.write( "p(6) = C(6,6) * .38^6 * .62^0<BR>\n" );
document.write( "you can't solve the problem without using the formula.<BR>\n" );
document.write( "when you apply the formula,  you get the following:<BR>\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( "x   (n-x) C(6,x)  p^x           q^(n-x)       p^x*q^(n-x)     C(6,x)*p^x*q^(n-x)\r\n" );
document.write( "0   6     1       1             0.056800236   0.056800236     0.056800236\r\n" );
document.write( "1   5     6       0.38          0.091613283   0.034813048     0.208878286\r\n" );
document.write( "2   4     15      0.1444        0.14776336    0.021337029     0.320055438\r\n" );
document.write( "3   3     20      0.054872      0.238328      0.013077534     0.26155068\r\n" );
document.write( "4   2     15      0.02085136    0.3844        0.008015263     0.120228942\r\n" );
document.write( "5   1     6       0.007923517   0.62          0.00491258      0.029475482\r\n" );
document.write( "6   0     1       0.003010936   1             0.003010936     0.003010936\r\n" );
document.write( "						\r\n" );
document.write( "                  sum of all probabilities equals >>>>>>>>>   1\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "you now have all the information you need to solve the problem.<BR>\n" );
document.write( "the problem states:<BR>\n" );
document.write( "IF SIX WOMEN AGED 85 ARE RANDOMLY SELECTED WHAT IS THE PROBABILITY THAT FEWER THAN TWO OF THEM WILL SUFFER (OR HAVE SUFFERED) A HIP FRACTURE DUE TO OSTEOPOROSIS<BR>\n" );
document.write( "if fewer than 2 of them suffer, then that would be equal to the probability of p(0) + p(1).<BR>\n" );
document.write( "from the chart, p(0) = 0.056800236 and p(1) = 0.208878286<BR>\n" );
document.write( "add these together and you get the probability that fewer than 2 will suffer is equal to .265678522.<BR>\n" );
document.write( "you only need to calculate the probability of 0 or 1 sufferers because the problem stated that you wanted the probability that fewer than 2 suffered.<BR>\n" );
document.write( "i shows you the whole table to show you how the formula works and to demonstrate that the total probability had to be equal to 1 as it was based on the use of those formulas.<BR>\n" );
document.write( "in the table, that last column on the right is equal to p(x).<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "when x = 0, p(x) = 0.056800236<BR>\n" );
document.write( "when x = 6, p(6) = 0.003010936 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );