document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196891>Question 1196891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that one adult with smart phones are renewly selected 41% use them in meetings or class. If 6 adult smartphone users are randomly selected find the probability that at least 4 of them use their smart phone in meetings or classes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829936 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "When I searched out part of your problem, I came across this exact wording \"Assume that when adults with smartphones are randomly selected, 51% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes.\"\r<BR>\n" );
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document.write( "I'll assume that your problem fits a similar format.\r<BR>\n" );
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document.write( "Question:<BR>\n" );
document.write( "Assume that when adults with smartphones are randomly selected, 41% use them in meetings or classes. If 6 adult smartphone users are randomly selected find the probability that at least 4 of them use their smart phone in meetings or classes.\r<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "n = 6 = sample size<BR>\n" );
document.write( "p = 0.41 = probability someone uses a smartphone in meetings or in class\r<BR>\n" );
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document.write( "Let's consider the case where exactly x = 4 people use a smartphone during meetings or in class<BR>\n" );
document.write( "Use the nCr combination formula to find that 6C4 = 15\r<BR>\n" );
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document.write( "The scratch work is shown below<BR>\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "6 C 4 = (6!)/(4!*(6-4)!)<BR>\n" );
document.write( "6 C 4 = (6!)/(4!*2!)<BR>\n" );
document.write( "6 C 4 = (6*5*4!)/(4!*2!)<BR>\n" );
document.write( "6 C 4 = (6*5)/(2!)<BR>\n" );
document.write( "6 C 4 = (6*5)/(2*1)<BR>\n" );
document.write( "6 C 4 = (30)/(2)<BR>\n" );
document.write( "6 C 4 = 15<BR>\n" );
document.write( "There are 15 ways to select four from a pool of six, where order doesn't matter. \r<BR>\n" );
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document.write( "Then use the binomial distribution formula<BR>\n" );
document.write( "P(x) = (n C x)*(p)^(x)*(1-p)^(n-x)<BR>\n" );
document.write( "P(4) = (6 C 4)*(0.41)^(4)*(1-0.41)^(6-4)<BR>\n" );
document.write( "P(4) = (6 C 4)*(0.41)^(4)*(0.59)^(2)<BR>\n" );
document.write( "P(4) = (15)*(0.41)^(4)*(0.59)^2<BR>\n" );
document.write( "P(4) = (15)*(0.02825761)*(0.3481)<BR>\n" );
document.write( "P(4) = 0.147547110615<BR>\n" );
document.write( "The probability that exactly 4 people use their phone during meetings or in class is roughly 0.147547110615\r<BR>\n" );
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document.write( "Repeat similar steps for x = 5 and x = 6<BR>\n" );
document.write( "I'll skip the steps and jump to the results of each<BR>\n" );
document.write( "P(5) = 0.041013095154<BR>\n" );
document.write( "P(6) = 0.004750104241\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x+%3E=+4%29+=+P%284%29+%2B+P%285%29+%2B+P%286%29 ALIGN=MIDDLE  ALT=\"P%28x+%3E=+4%29+=+P%284%29+%2B+P%285%29+%2B+P%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x+%3E=+4%29+=+0.147547110615%2B0.041013095154%2B0.004750104241 ALIGN=MIDDLE  ALT=\"P%28x+%3E=+4%29+=+0.147547110615%2B0.041013095154%2B0.004750104241\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x+%3E=+4%29+=+0.19331031001 ALIGN=MIDDLE  ALT=\"P%28x+%3E=+4%29+=+0.19331031001\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The probability of at least 4 people, out of 6 total in the sample size, using a smartphone during meetings or class is roughly 0.19331031001<BR>\n" );
document.write( "When rounding to something like four decimal places, we get roughly 0.1933<BR>\n" );
document.write( "Round the answer however your teacher instructs.<BR>\n" );
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