document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203585>Question 1203585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The time required to complete a college achievement test was foundto be normally\r<BR>\n" );
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document.write( "distributed, with a mean of 110 minutes and standard deviation of20 minutes.\r<BR>\n" );
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document.write( "(a) What proportion of the students will ?nish within 2 hours (120minutes)?\r<BR>\n" );
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document.write( "(b) What proportion of the students will ?nish at exactly 2hours?\r<BR>\n" );
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document.write( "(c) When should the test be terminated to allow just enough timefor 90% of the\r<BR>\n" );
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document.write( "students to complete the test </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839259 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 110 minutes.<BR>\n" );
document.write( "standard deviation is 20 minutes.\r<BR>\n" );
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document.write( "use the z-score formula.<BR>\n" );
document.write( "it is z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard deviation<BR>\n" );
document.write( "x is the student score\r<BR>\n" );
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document.write( "The time required to complete a college achievement test was found to be normally distributed, with a mean of 110 minutes and standard deviation of20 minutes.\r<BR>\n" );
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document.write( "(a) What proportion of the students will finish within 2 hours (120 minutes)?\r<BR>\n" );
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document.write( "z = (120 - 110) / 20 = .5<BR>\n" );
document.write( "area to the left of a z-score of .5 = .6915.<BR>\n" );
document.write( "this means that 69.15% of the participants will complete the test in 120 minutes or less.\r<BR>\n" );
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document.write( "(b) What proportion of the students will finish at exactly 2 hours?\r<BR>\n" );
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document.write( "the theory says that, because this is a continuous curve, the probability of getting exactly 120 minutes is 0.\r<BR>\n" );
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document.write( "here's  refference that addresses that issue.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_probability/bs704_probability8.html#:~:text=Note%20that%20with%20the%20normal,is%20%3C%2029%20is%2050%25.\" target = \"_blanak\">https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_probability/bs704_probability8.html#:~:text=Note%20that%20with%20the%20normal,is%20%3C%2029%20is%2050%25.</a>\r<BR>\n" );
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document.write( "the particular statement in that reference is:<BR>\n" );
document.write( "Note that with the normal distribution the probability of having any exact value is 0 because there is no area at an exact BMI value, so in this case, the probability that his BMI = 29 is 0, but the probability that his BMI is <29 or the probability that his BMI is < 29 is 50%.\r<BR>\n" );
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document.write( "(c) When should the test be terminated to allow just enough time for 90% of the<BR>\n" );
document.write( "students to complete the test.\r<BR>\n" );
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document.write( "z-score that has 90% of the area under the normal distribution curve to the left of it is equal to 1.2816.<BR>\n" );
document.write( "z-score formula becomes:<BR>\n" );
document.write( "1.2816 = (x - 110) / 20<BR>\n" );
document.write( "solve for x to get x = 20 * 1.2816 + 110 = 135.632.<BR>\n" );
document.write( "that's the number of minutes that the test would be terminated so that 90% of the participants will have been able to complete the test.<BR>\n" );
document.write( "any rounding should be rounding up to ensure at least 90%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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