document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130143>Question 130143</A>: <I><SPAN STYLE=\"word-break: break-all;\"> question 1\r<BR>\n" );
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document.write( "According to a survey, 50% of employees in banking sector are satisfied with their jobs. Assume this is the true proportion of all satisfied employees in banking sector. Let p be the proportion of banking sector employees in a random sample of 1000 who are satisfied with their jobs.<BR>\n" );
document.write( "a) Describe the shape of the sampling distribution for the sample proportion.<BR>\n" );
document.write( "b) Find the mean and standard deviation of the sample proportion, p.\r<BR>\n" );
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document.write( "questions 2\r<BR>\n" );
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document.write( "Assume that the weights of all mini-packages of a certain brand biscuits are normally distributed with mean of 32 grams and standard deviation of 0.3 grams. Find the probability that the mean weightx, of a random sample of 20 packages of this brand of biscuits will be between 31.8 and 31.9 grams. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95065 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=95065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> According to a survey, 50% of employees in banking sector are satisfied with their jobs. Assume this is the true proportion of all satisfied employees in banking sector. Let p be the proportion of banking sector employees in a random sample of 1000 who are satisfied with their jobs.<BR>\n" );
document.write( "a) Describe the shape of the sampling distribution for the sample proportion.<BR>\n" );
document.write( "The sample proportions are normally distributed.<BR>\n" );
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document.write( "b) Find the mean and standard deviation of the sample proportion, p.<BR>\n" );
document.write( "The mean is 50% or 1/2; The standard deviation is sqrt{pq/n] <BR>\n" );
document.write( "= sqrt[(1/2)^2/1000] = [(1/2)/10]sqrt(1/10) = (1/20)[sqrt(10)/10]<BR>\n" );
document.write( "= (1/200)sqrt(10)<BR>\n" );
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document.write( "questions 2 <BR>\n" );
document.write( "Assume that the weights of all mini-packages of a certain brand biscuits are normally distributed with mean of 32 grams and standard deviation of 0.3 grams. Find the probability that the mean weightx, of a random sample of 20 packages of this brand of biscuits will be between 31.8 and 31.9 grams.<BR>\n" );
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document.write( "Find the z-score of 31.8 and 31.9<BR>\n" );
document.write( "z(31.8) = (31.8-32)/[0.3/sqrt(20)] = -0.2*sqrt(20)/0.3 = -2.9814<BR>\n" );
document.write( "z(31.9) = (31.9-32)/[0.3/sqrt(20)] = -0.1*sqrt(20)/0.3 = -1.490712<BR>\n" );
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document.write( "P(31.8 < x < 31.9) = P(-2.9814 < z < -1.4907) = 0.06658...<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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