document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765751>Question 765751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Reading readiness of preschoolers from an impoverished neighborhood (n = 20) was measured using a standardized test.  Nationally, the mean on this test for preschoolers is 30.9, with SD = 2.08. \r<BR>\n" );
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document.write( "a.	Children below the 30th percentile (in the bottom 30%) are in need of special assistance prior to attending school.  What raw score marks the cut-off score for these children?  (8 pts)\r<BR>\n" );
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document.write( "(What I came up with- Z-Score=-2.75  X=30.9+2.08(-2.75)=25.18  Cut Off is 25.18)\r<BR>\n" );
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document.write( "b.	What percentage of children score between 25 and 28.5? (8 pts)<BR>\n" );
document.write( "(what I came up with- Z= (25-30.9)/2.08=-2.83   Z= (28.5-30.9)/2.08=-1.15<BR>\n" );
document.write( "-2.83+-1.15=-3.98   50-3.98=46.02      46.02% score between 25 and 28.5)\r<BR>\n" );
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document.write( "c.	How many children would we expect to find with scores between 28 and 31.5?(8 pts)<BR>\n" );
document.write( "(What I came up With- Z=(28-30.9)/2.08=-1.39     Z=(31.5-30.9)/2.08=.28<BR>\n" );
document.write( " -1.39+.28=-1.11      Z-Score=2.29, <BR>\n" );
document.write( "X=30.9+2.08(2.29)= 35.66       36 Children have scores between 28 and 31.5)\r<BR>\n" );
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document.write( "d.	Children in the top 25% are considered accelerated readers and qualify for different placement in school.  What raw score would mark the cutoff for such placement? (11 pts)\r<BR>\n" );
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document.write( "(What I came up With- . Z-Score=2.81 X=30.9+2.08(2.81)=9.74  Cut-Off is 9.74)<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 #466387 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=466387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Reading readiness of preschoolers from an impoverished neighborhood (n = 20) was measured using a standardized test. Nationally, the mean on this test for preschoolers is 30.9, with SD = 2.08. \r<BR>\n" );
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document.write( "a. Children below the 30th percentile (in the bottom 30%) are in need of special assistance prior to attending school. What raw score marks the cut-off score for these children? (8 pts)<BR>\n" );
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document.write( "Find the z-score with a left tail of 30%::<BR>\n" );
document.write( "invNorm(0.30) = -0.5244<BR>\n" );
document.write( "Find the score using x = z*s + u<BR>\n" );
document.write( "x = -0.5244*2.08+30.9 = 29.81<BR>\n" );
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document.write( "(What I came up with- Z-Score=-2.75 X=30.9+2.08(-2.75)=25.18 Cut Off is 25.18)<BR>\n" );
document.write( "Comment: You found the z-score with a left tail of 0.003.<BR>\n" );
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document.write( "b. What percentage of children score between 25 and 28.5? (8 pts)<BR>\n" );
document.write( "Z(25)= (25-30.9)/2.08=-2.83 <BR>\n" );
document.write( "Z(28.5)= (28.5-30.9)/2.08=-1.15<BR>\n" );
document.write( "P(25< x < 28.5) = P(-2.83< z < -1.15) = normalcdf(-2.83,-1.15) = 0.1227<BR>\n" );
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document.write( "c. How many children would we expect to find with scores between 28 and 31.5?(8 pts)<BR>\n" );
document.write( "(What I came up With- <BR>\n" );
document.write( "Z=(28-30.9)/2.08=-1.39 <BR>\n" );
document.write( "Z=(31.5-30.9)/2.08=.28<BR>\n" );
document.write( "P(-1.39< z < 0.28) = normalcdf(-1.39,0.28) = 0.5280<BR>\n" );
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document.write( "# of children = 0.5280*20 = 11 when rounded up<BR>\n" );
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document.write( "d. Children in the top 25% are considered accelerated readers and qualify for different placement in school. What raw score would mark the cutoff for such placement? (11 pts) <BR>\n" );
document.write( "Find the z-score wit a left tail of 75%<BR>\n" );
document.write( "invNorm(0.75) = 0.6745<BR>\n" );
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document.write( "Find the correspondig score:<BR>\n" );
document.write( "x = z*s + u<BR>\n" );
document.write( "x = 0.6745*2.08+30.9 = 32.3<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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