document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205509>Question 1205509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you solve the question below, I'll be appreciated.\r<BR>\n" );
document.write( "\n" );
document.write( "An exam consists of 42 multiple-choice questions. Each question has a choice of five answers, only one of which is correct. For each correct answer, a candidate gets 1 mark, and no penalty is applied for getting an incorrect answer. A particular candidate answers each question purely by guess-work.\r<BR>\n" );
document.write( "\n" );
document.write( "Using Normal approximation to Binomial distribution with continuity correction, what is the estimated probability this student obtains a score greater than or equal to 10? Please use R to obtain probabilities and keep at least 6 decimal places in intermediate steps.\r<BR>\n" );
document.write( "\n" );
document.write( "A. 0.6643<BR>\n" );
document.write( "B. 0.2089<BR>\n" );
document.write( "C. 0.4059<BR>\n" );
document.write( "D. 0.3357<BR>\n" );
document.write( "E. 0.5650 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842361 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=842361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> answer is selection D.<BR>\n" );
document.write( "i did it two ways.<BR>\n" );
document.write( "first way was direct, using the binomial distribution formula, in excel.<BR>\n" );
document.write( "that formula is p(x) = p^x * q^(n-x) * c(n,x)<BR>\n" );
document.write( "all values of p(10) to p(42) are summed up to get the probability of x being greater than or equal to 10.<BR>\n" );
document.write( "the probability of x being greater than or equal to 10 was equal to  0.324376129<BR>\n" );
document.write( "i then used normal approximation to the binomial.<BR>\n" );
document.write( "p(x >= 10) = selection D =  0.3357<BR>\n" );
document.write( "the normal approximation won't be exact, but it'll be close.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here are the results using the normal distribution calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a><BR>\n" );
document.write( "here are the results.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/010201.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the mean was set at 10<BR>\n" );
document.write( "the standard deviation was set at sqrt(42 * .2 * .8) = 2.592296\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here is a reference on normal approximation of the binomial.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/06%3A_Continuous_Random_Variables_and_the_Normal_Distribution/6.04%3A_Normal_Approximation_to_the_Binomial_Distribution\" target = \"_blank\">https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/06%3A_Continuous_Random_Variables_and_the_Normal_Distribution/6.04%3A_Normal_Approximation_to_the_Binomial_Distribution</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "with proportions, the mean is equal to n * p.<BR>\n" );
document.write( "in this case it was 42 * .2 = 8.4<BR>\n" );
document.write( "the standard error is equal to sqrt(n * p * q) = sqrt(42 * .2 * .8).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );