document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136954>Question 1136954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tony’s Pizza Company finds that 65% of the general population likes pepperoni pizza. I buy pizza for 56 of my intro stats students and it turns out that only 30 of these students like pepperoni pizza.<BR>\n" );
document.write( "(a) Using the normal approximation to the binomial distribution, what is the probability of getting 30 or fewer students who like pepperoni pizza in a randomly selected group of 56 students? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754780 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=754780\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = .65<BR>\n" );
document.write( "q = 1 - p = .35<BR>\n" );
document.write( "n = 56<BR>\n" );
document.write( "x = 30\r<BR>\n" );
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document.write( "in the binomial distribution, mean of the sample = n * p = .65 * 56 = 36.4\r<BR>\n" );
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document.write( "standard deviation of the distribution of sample means is equal to sqrt( n * p * q) = sqrt( 56 * .65 * .34) = sqrt(12.74) = 3.56931366.\r<BR>\n" );
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document.write( "using the online normal distribution calculator found at <a  rel=nofollow HREF= \"\" target = \"_blank\"></a>, you would find that the probability of 30 or fewer of the students out of 56 students liking pepperoni pizza is equal to .0492.\r<BR>\n" );
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document.write( "i used excel to determine what the actual probability would be.\r<BR>\n" );
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document.write( "in excel, i used the binomial probability formula of p(x) = p^x * q^(n-x) * c(n,x).\r<BR>\n" );
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document.write( "n is equal to 56.<BR>\n" );
document.write( "p is equal to .65<BR>\n" );
document.write( "q is equal to .35<BR>\n" );
document.write( "x is equal to the number of people who like pepperoni pizza.\r<BR>\n" );
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document.write( "excel told me that the probability of 30 or fewer liking pepperoni pizza was .051113.\r<BR>\n" );
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document.write( "there is an online calculator that tells you what the binomial probability would be and also what the normal approximation to the binomial probability would be.\r<BR>\n" );
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document.write( "that calculator can be found at <a  rel=nofollow HREF= \"https://homepage.divms.uiowa.edu/~mbognar/applets/binnormal.html\" target = \"_blank\">https://homepage.divms.uiowa.edu/~mbognar/applets/binnormal.html</a>\r<BR>\n" );
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document.write( "it confirmed that the normal approximation to the binomial probability is .0492 and the binomial probaiblity is .051113 as i had determined from the use of excel.\r<BR>\n" );
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document.write( "here's a display of use of the normal distribution calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/031911.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here's a display of use of the binomial probability and normal approximation calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/031912.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here's a display of the use of excel.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/031913.jpg\" alt=\"$$$\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/031914.jpg\" alt=\"$$$\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/031915.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the excel is the most detailed because it shows the probability of every x from 0 to 56.\r<BR>\n" );
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