document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=923678>Question 923678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 0.8 lb. and 2 oz., or 420 grams. Assume the standard deviation of the weights is 21 grams and a sample of 45 loaves is to be randomly selected. <BR>\n" );
document.write( "(a) This sample of 45 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution. <BR>\n" );
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document.write( "skewed right \r<BR>\n" );
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document.write( "approximately normal     \r<BR>\n" );
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document.write( "skewed left \r<BR>\n" );
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document.write( "chi-square \r<BR>\n" );
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document.write( "Correct: Your answer is correct. .<BR>\n" );
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document.write( " (b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.) <BR>\n" );
document.write( "  grams\r<BR>\n" );
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document.write( " (c) Find the standard error of this sampling distribution. (Give your answer correct to two decimal places.) <BR>\n" );
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document.write( " (d) What is the probability that this sample mean will be between 416 and 424? (Give your answer correct to four decimal places.) <BR>\n" );
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document.write( " (e) What is the probability that the sample mean will have a value less than 410? (Give your answer correct to four decimal places.) <BR>\n" );
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document.write( " (f) What is the probability that the sample mean will be within 3 grams of the mean? (Give your answer correct to four decimal places.) <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 #560244 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=560244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 420 grams. Assume the standard deviation of the weights is 21 grams<BR>\n" );
document.write( " sample of 45 loaves is to be randomly selected. <BR>\n" );
document.write( "(b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.) 420gm\r<BR>\n" );
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document.write( " (c) Find the standard error of this sampling distribution. (Give your answer correct to two decimal places.) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2Fsqrt%2845%29 ALIGN=MIDDLE  ALT=\"21%2Fsqrt%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.13\r<BR>\n" );
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document.write( " (d) What is the probability that this sample mean will be between 416 and 424? (Give your answer correct to four decimal places.) <BR>\n" );
document.write( "z = -4/3.13 = -.278   and z = 4/313 = .278<BR>\n" );
document.write( "P(416 < x < 424)= normalcdf(-.278, .278) = .6068\r<BR>\n" );
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document.write( " (e) What is the probability that the sample mean will have a value less than 410? (Give your answer correct to four decimal places.) <BR>\n" );
document.write( "P(x-bar < 410) =P(z < -10/3.13)= .0007\r<BR>\n" );
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document.write( " (f) What is the probability that the sample mean will be within 3 grams of the mean? (Give your answer correct to four decimal decimal places.) <BR>\n" );
document.write( "P (417 x < 423) = normalcdf( -3/3.13, 3/3.13)= .6622 </SPAN>\n" );
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