document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=846128>Question 846128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 22. Smokers, According to Information Please Almanac, 80% of adult smokers started smoking before they were 18 years old. Suppose 100 smokers 18 years old or older are randomly selected. Use the normal approximation to the binomial to:<BR>\n" );
document.write( "(a) Approximate the probability that exactly 80 of them started smoking before they were 18 years old.<BR>\n" );
document.write( "(b) Approximate the probability that at least 80 of them started smoking before they were 18 years old.<BR>\n" );
document.write( "(c) Approximate the probability that fewer than 70 of them started smoking before they were 18 years old. <BR>\n" );
document.write( "(d) Approximate the probability that between 7- and 90 of them, inclusive, started smoking before they were 18 years old. <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 #509684 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=509684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Smokers, According to Information Please Almanac, 80% of adult smokers started smoking before they were 18 years old. <BR>\n" );
document.write( "Suppose 100 smokers 18 years old or older are randomly selected.<BR>\n" );
document.write( "mean = np = 100*0.80 = 80<BR>\n" );
document.write( "std = sqrt(npq) = sqrt(80*0.20) = sqrt(16) = 4 <BR>\n" );
document.write( "Use the normal approximation to the binomial to:<BR>\n" );
document.write( "(a) Approximate the probability that exactly 80 of them started smoking before they were 18 years old.<BR>\n" );
document.write( "Find P(79.5 < x < 80.5)<BR>\n" );
document.write( "z(79.5) = (79.5-80)/4 = -0.5/4 = -0.125<BR>\n" );
document.write( "z(80.5) = (80.5-80)/4 = +0.125<BR>\n" );
document.write( "----<BR>\n" );
document.write( "P(x = 80) = P(-0.125< z < 0.125) = 0.3867 <BR>\n" );
document.write( "(b) Approximate the probability that at least 80 of them started smoking before they were 18 years old.<BR>\n" );
document.write( "P(x >= 80) = P(z >= 0.125) = 0.45<BR>\n" );
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document.write( "(c) Approximate the probability that fewer than 70 of them started smoking before they were 18 years old.<BR>\n" );
document.write( "z(69.5) = (69.5-80)/4 = -10.5/4 = -2.625<BR>\n" );
document.write( "P(x <= 69.5) = P(z <= -2.625) = 0.004<BR>\n" );
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document.write( "(d) Approximate the probability that between 7- and 90 of them, inclusive, started smoking before they were 18 years old.<BR>\n" );
document.write( "Find (6.5 < x < 90.5)<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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