document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=754925>Question 754925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> .  (a) With n = 14 and p = 0.3, find the binomial probability P(9) by using a binomial probability table.<BR>\n" );
document.write( "        (b) If np &#8805;5 and nq &#8805;5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial; if np < 5 or nq < 5, then state that the normal approximation cannot be used.<BR>\n" );
document.write( "(a) Find the probability by using a binomial probability table.<BR>\n" );
document.write( "P(9) = [  ] (Round to four decimal places as needed).<BR>\n" );
document.write( "(b) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.<BR>\n" );
document.write( "A.  P(9) = [  ] (Round to four decimal places as needed)<BR>\n" );
document.write( "B.  The normal distribution cannot be used.\r<BR>\n" );
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document.write( "Also, <BR>\n" );
document.write( "If the random variable z is a Standard Normal Score, what is P(-2.00 &#8804; z &#8804; +2.00)? How did you find this probability?<BR>\n" );
document.write( "Find the z score for the standard normal distribution where:  P(z<+a) = 0.9625\r<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 #459434 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=459434\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) With n = 14 and p = 0.3, find the binomial probability P(9) by using a binomial probability table.<BR>\n" );
document.write( "P(x = 9) = 14C9*(0.3)^9*(0.7)^5 = binompdf(14,0.3,9) = 0.0066<BR>\n" );
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document.write( "(b) If np &#8805;5 and nq &#8805;5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial; if np < 5 or nq < 5, then state that the normal approximation cannot be used.<BR>\n" );
document.write( "mean = np = 14*0.3 = 4.2 ; std = sqrt[npq] = sqrt(4.2*0.7) = 1.7146<BR>\n" );
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document.write( "P(x = 9) = P(8.5< x <9.5)<BR>\n" );
document.write( "Find the z-values: <BR>\n" );
document.write( "z(8.5) = (8.5-4.2)/1.7146 = 2.5079<BR>\n" );
document.write( "z(9.5) = (9.5-4.2)/1.7146 = 3.0911<BR>\n" );
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document.write( " = P(2.5079< z <3.0911) = 0.0051<BR>\n" );
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document.write( " <BR>\n" );
document.write( "Also, <BR>\n" );
document.write( "If the random variable z is a Standard Normal Score, what is P(-2.00 &#8804; z &#8804; +2.00)? How did you find this probability?<BR>\n" );
document.write( "Ans: Using a TI-84 I get: normalcdf(-2,2) = 0.9545<BR>\n" );
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document.write( "Find the z score for the standard normal distribution where: P(z<+a) = 0.9625<BR>\n" );
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document.write( "Find the z-value with a left tail of 0.9625<BR>\n" );
document.write( "a = invNorm(0.9625) = 1.0875<BR>\n" );
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document.write( "cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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