document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086671>Question 1086671</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have probability 0.70 of germinating. The biologist plants 10 seeds. \r<BR>\n" );
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document.write( "A.What is the probability that exactly 8 seeds will germinate? Round your answer to the nearest thousandths.\r<BR>\n" );
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document.write( "B.What is the probability that at least 8 seeds will germinate? Round your answer to the nearest thousandth.\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 #700889 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700889\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( "A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have probability 0.70 of germinating. The biologist plants 10 seeds. <BR>\n" );
document.write( "A.What is the probability that exactly 8 seeds will germinate? Round your answer to the nearest thousandths.<BR>\n" );
document.write( "B.What is the probability that at least 8 seeds will germinate? Round your answer to the nearest thousandth.\r<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "To model a situation using the binomial distribution, the following criteria must be satisfied:<BR>\n" );
document.write( "1. Bernoulli trials, i.e. exactly two possible outcomes (germinate or not)<BR>\n" );
document.write( "2. Number of trials is known before and constant throught experiment, <BR>\n" );
document.write( "i.e. independent of outcomes (n=10 seeds planted)<BR>\n" );
document.write( "3. All trials are independent of each other (appropriate assumption for the current situation)<BR>\n" );
document.write( "4. Probability of success is known, and remain constant throughout trials. (p=0.7, given)<BR>\n" );
document.write( "Since all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given by<BR>\n" );
document.write( "P(x)=C(N,x)(p^x)(1-p)^(N-x)<BR>\n" );
document.write( "and,<BR>\n" );
document.write( "C(N,x) is number of combinations of selecting x objects out of N.<BR>\n" );
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document.write( "(A) P(x=8)=C(10,8)p^x(1-p)^(n-x)<BR>\n" );
document.write( "=45*0.7^8(1-0.7)^2<BR>\n" );
document.write( "=45*.05764801*0.09<BR>\n" );
document.write( "=0.233474<BR>\n" );
document.write( "(B) <BR>\n" );
document.write( "P(at least 8 seeds will germinate)<BR>\n" );
document.write( "=P(8)+P(9)+P(10)<BR>\n" );
document.write( "=0.233474+0.121061+0.028248<BR>\n" );
document.write( "=0.38278 </SPAN>\n" );
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