document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=761465>Question 761465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble on these two problems..\r<BR>\n" );
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document.write( "Students in a particular class complete an exam in a mean time of 45 minutes with a standard deviation of 8 minutes.  If student is selected at random, what is the probability he/she will complete it in less than 40 minutes?\r<BR>\n" );
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document.write( "An insurance company claims that a customer can save an average of at least $400 per year on car insurance.  A sample of 22 customers showed that the mean amount saved was $375 per year with a standard deviation of $48.  Use a level of significance of 0.01 to test the insurance company’s claim.  \r<BR>\n" );
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document.write( "Thanks alot! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463364 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=463364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Students in a particular class complete an exam in a mean time of 45 minutes with a standard deviation of 8 minutes. If student is selected at random, what is the probability he/she will complete it in less than 40 minutes? <BR>\n" );
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document.write( "z(40) = (40-45)/8 = -5/8<BR>\n" );
document.write( "P(x < 40 min) = P(z < -5/8) = normalcdf(-100,-5/8) = 0.2660<BR>\n" );
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document.write( "An insurance company claims that a customer can save an average of at least $400 per year on car insurance. A sample of 22 customers showed that the mean amount saved was $375 per year with a standard deviation of $48. Use a level of significance of 0.01 to test the insurance company’s claim.<BR>\n" );
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document.write( "Ho: u < 400<BR>\n" );
document.write( "H1: u >= 400 (claim)<BR>\n" );
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document.write( "t(375) = (375-400)/[48/sqrt(22)] = -2.4429<BR>\n" );
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document.write( "p-value = P(x-bar >= 400) = P(t >= -2.4429 when df = 21) = tcdf(-2.4429,100,21)<BR>\n" );
document.write( "= 0.9883<BR>\n" );
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document.write( "Conclusion: Since the p-value is greater than 1%, fail to reject Ho.<BR>\n" );
document.write( "The test results do not support the claim.<BR>\n" );
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document.write( "cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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