document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195496>Question 1195496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ok, this is a big one. i need help with all of them, please and thank you. i wonder if i could figure this out on wolfram alpha or desmos! \r<BR>\n" );
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document.write( "Scores for a common standardized college aptitude test are normally distributed with a mean of 502 and a standard deviation of 111 . Randomly-selected women are given a Preparation Course before taking this test.\r<BR>\n" );
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document.write( "a) If one of the women is randomly selected, find the probability that her score is at least 565.7. Enter your answer as a number accurate to 4 decimal places. \r<BR>\n" );
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document.write( "b) If nineteen of the women are randomly selected, find the probability that their mean score is at least 565.7. Enter your answer as a number accurate to 4 decimal places.\r<BR>\n" );
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document.write( "c) I initially assumed that the Preparation Course had no effect on people's test scores. A random sample of nineteen women does result in a mean score of more than 565.7. Is there strong evidence to support a claim that I was wrong -- and the Preparation Course is actually effective? Yes or No\r<BR>\n" );
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document.write( "Yes. The probability indicates that -- if the Preparation Course has no effect -- it is highly unlikely that a randomly selected group of women would get a mean higher than 565.7 by chance.\r<BR>\n" );
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document.write( "No. The probability indicates that -- even if the Preparation Course has no effect -- it isn't unlikely to randomly select a group of women with a mean higher than  <BR>\n" );
document.write( "565.7 by chance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828014 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=828014\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for a single sample, your z-score is equal to (565.7 - 502) / 111 = .5738738739, rounded to 10 decimal places.<BR>\n" );
document.write( "the probability she will get a z-score less than that is equal to .7169734661.<BR>\n" );
document.write( "the probability she will not get a z-score less than that is equal to 1 minus .7169734661 = .2830265339.<BR>\n" );
document.write( "that's the probability she will get a z-score greater than or equal to that.<BR>\n" );
document.write( "all numbers are rounded to the number of decimal places that can be displayed from the calculator used.<BR>\n" );
document.write( "round to 4 decimal places to get .2830.\r<BR>\n" );
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document.write( "for a single sample, you use the standard deviation.<BR>\n" );
document.write( "for the mean of a sample of size greater than 1, you use the standard error.<BR>\n" );
document.write( "if the sample size is 19, then the standard error is equal to the standard deviation divided by the square root of the sample size = 111 / sqrt(19) = 25.46514646.<BR>\n" );
document.write( "the z-score is equal to (565.7 - 502) / 25.46514646 = 2.501458223.<BR>\n" );
document.write( "the probability she will get a z-score less than that is equal to .9938158335.<BR>\n" );
document.write( "the probability that she will not get a z-score less than that is equal to 1 - .9938158335 = .006184665.<BR>\n" );
document.write( "that's the probability she will get a z-score greater than or equal to that.<BR>\n" );
document.write( "round to 4 decimal places to get .0062.\r<BR>\n" );
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document.write( "a probability of .0062 is a very small probability.<BR>\n" );
document.write( "that means that it is highly unlikely that a sample of 19 women will have a mean score of 565.7 or greater by chance alone.<BR>\n" );
document.write( "that means that, if the mean of the sample of 19 women was 565.7, then something else might be influencing that other than chance.<BR>\n" );
document.write( "a likely culprit would be that the preparation course did have an effect on their scores.\r<BR>\n" );
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document.write( "i used the ti-84 plus calculator to get these results.<BR>\n" );
document.write( "you can get comparable results using the calculator at <a  rel=nofollow HREF= \"https://www.calculator.net/z-score-calculator.html\" target = \"_blank\">https://www.calculator.net/z-score-calculator.html</a>\r<BR>\n" );
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document.write( "results from using this calculator are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/071501.jpg\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/071502.jpg\" >\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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