document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=806821>Question 806821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. The Marketing Manager at Smart Post Delivery Company is analyzing the performance of a new product, The Mega Box. This is a very sturdy padded box inside which any item can be placed and shipped without breaking. The manager has collected data from past delivery reports and found that 1% of the items placed in the Mega Box broke during shipping. <BR>\n" );
document.write( "(i) If a random sample of 12 items placed in the Mega Box was selected, what is the probability that at most two items would break during shipping? 	                                                            <BR>\n" );
document.write( "(ii) What is the mean number of items that would break during shipping?	 \r<BR>\n" );
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document.write( "2. Smart Snacks recently introduced a new snack product to its customers, the Chocolate Crisp Sandwich. The number of sandwiches sold over the last 5 days is described by the following probability distribution.<BR>\n" );
document.write( "Number of sandwiches, x 	15	20	25	30	35<BR>\n" );
document.write( "Probability, P(x)	       0.25	0.40	0.15   0.12      *<BR>\n" );
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document.write( "(i)	What is the probability that 35 sandwiches were sold. 			<BR>\n" );
document.write( "(ii)	 What is the probability that less than 25 sandwiches were sold. 		<BR>\n" );
document.write( "(iii)	Calculate the expected number of sandwiches to be sold.	<BR>\n" );
document.write( "(iv)	Calculate the standard deviation for the number of sandwiches sold.	<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 #486058 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=486058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The manager has collected data from past delivery reports and found that 1% of the items placed in the Mega Box broke during shipping. <BR>\n" );
document.write( "(i) If a random sample of 12 items placed in the Mega Box was selected, what is the probability that at most two items would break during shipping?<BR>\n" );
document.write( "Binomial Problem with n = 12 and p(broke) = 0.01<BR>\n" );
document.write( "P(0<= x <=2) = binomcdf(12,0.01,2) = 0.9999<BR>\n" );
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document.write( "(ii) What is the mean number of items that would break during shipping?<BR>\n" );
document.write( "mean = np = 12*0.01 = 0.12<BR>\n" );
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document.write( " <BR>\n" );
document.write( "2. Smart Snacks recently introduced a new snack product to its customers, the Chocolate Crisp Sandwich. The number of sandwiches sold over the last 5 days is described by the following probability distribution.<BR>\n" );
document.write( "Number of sandwiches, x    15   20   25   30  35<BR>\n" );
document.write( "Probability,        P(x) 0.25 0.40 0.15 0.12 *<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(i) What is the probability that 35 sandwiches were sold.<BR>\n" );
document.write( "Ans:: 1 -(0.25+0.40+0.15+0.12) = 0.08<BR>\n" );
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document.write( "(ii) What is the probability that less than 25 sandwiches were sold.<BR>\n" );
document.write( "Ans: 0.25+0.40 = 0.65<BR>\n" );
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document.write( "(iii) Calculate the expected number of sandwiches to be sold.<BR>\n" );
document.write( "Ans: E(x) = 15*0.25+20*0.40+25*0.15+30*0.12+35*0.08 = 21.9<BR>\n" );
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document.write( "(iv) Calculate the standard deviation for the number of sandwiches sold.<BR>\n" );
document.write( "Ans:: std = 7.9057<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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