document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111413>Question 1111413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help figuring out how to get the new grade by using the z score of the new mean. Help please!\r<BR>\n" );
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document.write( "	Suppose a professor gives an exam to a class of 40 students and the scores are as follows.\r<BR>\n" );
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document.write( "35	44	46	47	47	48	49	51	53	54<BR>\n" );
document.write( "55	55	57	57	57	58	59	59	59	59<BR>\n" );
document.write( "60	60	60	60	60	62	62	62	64	68<BR>\n" );
document.write( "69	70	72	73	73	75	75	77	82	88\r<BR>\n" );
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document.write( "Question....\r<BR>\n" );
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document.write( "3.	Suppose the professor wants the final scores to have a mean of 75 and a standard deviation of 8.\r<BR>\n" );
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document.write( "To find a student’s new score, first calculate their z-score and then use the z-score along with the new mean and standard deviation to find their adjusted score. re-type the new scores below.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726414 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=726414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think what they're asking is the following.\r<BR>\n" );
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document.write( "the mean of the original data set is 60.525 and the standard deviation of the original data set is 10.818935945831.\r<BR>\n" );
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document.write( "the raw score of 35 would have a z-score of (35 - 60.525) / 10.818935945831, which is equal to -2.821441975\r<BR>\n" );
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document.write( "that z-score with a data set that has a mean of 75 and a standard deviation of 8 would have a raw score of -2.821441975 * 8 + 75 = 52.4284642\r<BR>\n" );
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document.write( "the formula to use for z-score is:\r<BR>\n" );
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document.write( "z = (x - m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score of the data set<BR>\n" );
document.write( "m is the mean of the data set<BR>\n" );
document.write( "s is the standard deviation of the data set.\r<BR>\n" );
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document.write( "if you know the z-score, you can use the z-score formula to find the raw score.\r<BR>\n" );
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document.write( "the formula to find the raw score, derived from the formula for the z-score, is:\r<BR>\n" );
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document.write( "x = z * s + m\r<BR>\n" );
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document.write( "assuming the z-score is -2.821441975 and the standard deviation is 10.818935945831 and the mean is 60.525, you would calculate the raw score as:\r<BR>\n" );
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document.write( "x = z * s + m.\r<BR>\n" );
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document.write( "this makes x = -2.821441975 * 10.818935945831 + 60.525 which results in:\r<BR>\n" );
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document.write( "x = 35.\r<BR>\n" );
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document.write( "this makes sense, since we started with a raw score of 35 and calculated the z-score of -2.821441975 from the mean of the original data set of 60.525 and the standard deviation of the original data set of 10.818935945831.\r<BR>\n" );
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document.write( "that same z-score, however, when it is part of a data set that has a mean of 75 and a standard deviation of 8 would generate a raw score as shown below.\r<BR>\n" );
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document.write( "x = -2.821441975 * 8 + 75 which makes the raw score equal to 52.4284642.\r<BR>\n" );
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document.write( "52.4284642 is the same number of standard deviations below the mean of 75 with a standard deviation of 8 as 35 is below the mean of 60.525 with a standard deviation of 10.818935945831.\r<BR>\n" );
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document.write( "since there was a large number of calculations, i did them in excel.\r<BR>\n" );
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document.write( "the following is the result of the excel calculations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/030601.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the first set of data are the original scores that were used to find the mean of 60.525 and the standard deviation of 10.818935945831.\r<BR>\n" );
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document.write( "the second set of data was the z-score derived from the original set of data and its associate mean and standard deviation.\r<BR>\n" );
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document.write( "the third set of data was the raw scores derived from the z-scores with a data set that has a mean of 75 and a standard deviation of 8.\r<BR>\n" );
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