document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=678262>Question 678262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of time it takes to fill an order at a local sandwich shop is normally distributed with a mean of 4.1 and standard deviation of 1.3 minutes. <BR>\n" );
document.write( "(a) what is the probability that the average waiting time for a random sample of ten customers is between 4.0 and 4.2 minutes?<BR>\n" );
document.write( "(b) the probability is 95% that the average waiting time for a random sample of ten customers is greater than how long? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #421284 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=421284\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length of time it takes to fill an order at a local sandwich shop is normally distributed with a mean of 4.1 and standard deviation of 1.3 minutes. <BR>\n" );
document.write( "(a) what is the probability that the average waiting time for a random sample of ten customers is between 4.0 and 4.2 minutes?<BR>\n" );
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document.write( "Note: std for all samples of size 10 = 1.3/sqrt(10)<BR>\n" );
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document.write( "z(4) = (4-4.1)/[1.3/sqrt(10)] = -0.2436<BR>\n" );
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document.write( "z(4.2) = (4.2-4.1)/(1.3/sqrt(10)) = +0.2436<BR>\n" );
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document.write( "P(4.0<= x-bar <=4.2) = P(-0.2436<= z <=0.2436) = 0.1925<BR>\n" );
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document.write( "(b) the probability is 95% that the average waiting time for a random sample of ten customers is greater than how long?<BR>\n" );
document.write( "Find the z-value with a left-tail of 5%:<BR>\n" );
document.write( "invNorm(0.05) = -1.645<BR>\n" );
document.write( "Find the corresponding wait time using x = z*s+u<BR>\n" );
document.write( "x = -1.645*(1.3/sqrt(10))+4.1 = 3.4237 minutes<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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