document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083275>Question 1083275</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A donut baker wants to ensure that the radius of its donuts is within +- 0.25cm. Based on past statistical studies, she knows that the donut’s radius has a standard deviation of 1.25cm. How many measurements should she take to ensure a 90 percent confidence in the radius of the donuts are within 0.25cm, rather than measure each and every donut that is baked? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697281 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=697281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use a <a  rel=nofollow HREF=\"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">stats table</a> to find that the critical value is roughly z = 1.645<BR>\n" );
document.write( "To find this value, locate \"90%\" at the bottom (in the Confidence Level section) and the value just above this entry is 1.645\r<BR>\n" );
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document.write( "The population standard deviation sigma is given to be sigma = 1.25\r<BR>\n" );
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document.write( "The margin of error desired is 0.25, so E = 0.25\r<BR>\n" );
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document.write( "We will plug z = 1.645, sigma = 1.25 and E = 0.25 into the <a  rel=nofollow HREF=\"https://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm\">formula</a> below to find n.\r<BR>\n" );
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document.write( "n = ( (z*sigma)/E )^2\r<BR>\n" );
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document.write( "n = ( (1.645*1.25)/0.25 )^2\r<BR>\n" );
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document.write( "n = ( 2.05625/0.25 )^2\r<BR>\n" );
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document.write( "n = ( 8.225 )^2\r<BR>\n" );
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document.write( "n = 67.650625\r<BR>\n" );
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document.write( "n = 68 ... round up to the nearest whole number\r<BR>\n" );
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document.write( "Min Sample Size: n = 68\r<BR>\n" );
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document.write( "So this means that she can use a sample size of 68 or larger.\r<BR>\n" );
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document.write( "She should take <font color=red>at least 68</font> measurements to ensure that the radius of the donuts is within +- 0.25cm. </SPAN>\n" );
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