document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=647522>Question 647522</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A psychologist studied self-esteem scores and found the sample data set to be normally distributed with a mean of 50 and a standard deviation of 5.\r<BR>\n" );
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document.write( "Part A**What raw score cuts off the bottom 10.03% of this distribution?\r<BR>\n" );
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document.write( "Steps:\r<BR>\n" );
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document.write( "What is the z-score that cuts off the bottom 10.03% of this distribution? \r<BR>\n" );
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document.write( "What is the raw score that cuts off the bottom 10.03% of this distribution? \r<BR>\n" );
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document.write( "Part B**What percentage of the scores is between 57.5 and 65?\r<BR>\n" );
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document.write( "Steps:\r<BR>\n" );
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document.write( "What is the z-score that corresponds to the raw score of 57.5? \r<BR>\n" );
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document.write( "What is the z-score that corresponds to the raw score of 65? \r<BR>\n" );
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document.write( "What percentage of the scores is between 57.5 and 65? \r<BR>\n" );
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document.write( "Part C:**A raw score of 35 is associated with what percentile?\r<BR>\n" );
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document.write( "What is the z-score associated with a raw score of 35? \r<BR>\n" );
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document.write( "A raw score of 35 is associated with what percentile? \r<BR>\n" );
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document.write( "Part D:**What raw scores mark the middle 34% of this distribution?<BR>\n" );
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document.write( "What are the z-scores that mark the middle 34% of this distribution? The z-score below the mean is  The z-score above the mean is <BR>\n" );
document.write( "What is the raw score below the mean?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406270 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=406270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A psychologist studied self-esteem scores and found the sample data set to be normally distributed with a mean of 50 and a standard deviation of 5. <BR>\n" );
document.write( "Part A**What raw score cuts off the bottom 10.03% of this distribution? <BR>\n" );
document.write( "Steps: <BR>\n" );
document.write( "What is the z-score that cuts off the bottom 10.03% of this distribution?<BR>\n" );
document.write( "z = invNorm(0.1003) = -1.280 <BR>\n" );
document.write( "What is the raw score that cuts off the bottom 10.03% of this distribution? <BR>\n" );
document.write( "x = zs + u<BR>\n" );
document.write( "x = -1.280*5 + 50 = 43.6<BR>\n" );
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document.write( "Part B**What percentage of the scores is between 57.5 and 65? <BR>\n" );
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document.write( "What is the z-score that corresponds to the raw score of 57.5?<BR>\n" );
document.write( "z(57.5) = (57.5-50)/5 = 1.5<BR>\n" );
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document.write( "What is the z-score that corresponds to the raw score of 65?<BR>\n" );
document.write( "z(65) = (65-50)/5 = 3<BR>\n" );
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document.write( "What percentage of the scores is between 57.5 and 65? <BR>\n" );
document.write( "P(57.5<= x <=65) = P(1.5<= z <=3) = 0.0655 = 6.55%<BR>\n" );
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document.write( "Part C:**A raw score of 35 is associated with what percentile? <BR>\n" );
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document.write( "What is the z-score associated with a raw score of 35?<BR>\n" );
document.write( "z(35) = (35-50)/5 = -15/5 = -3<BR>\n" );
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document.write( "A raw score of 35 is associated with what percentile?<BR>\n" );
document.write( "P(z < -3) = normalcdf(-100,-3) = 0.0013 = 0.13%<BR>\n" );
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document.write( "Part D:**What raw scores mark the middle 34% of this distribution?<BR>\n" );
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document.write( "What are the z-scores that mark the middle 34% of this distribution? <BR>\n" );
document.write( "The z-score below the mean is<BR>\n" );
document.write( "z = invNorm(.50-0.17) = -0.44<BR>\n" );
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document.write( "The z-score above the mean is +0.44<BR>\n" );
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document.write( "What is the raw score below the mean?<BR>\n" );
document.write( "x = -0.44*5+50 = 47.8<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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