SOLUTION: 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, wi

Question 765751: 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.

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)
(What I came up with- Z-Score=-2.75 X=30.9+2.08(-2.75)=25.18 Cut Off is 25.18)

b. What percentage of children score between 25 and 28.5? (8 pts)
(what I came up with- Z= (25-30.9)/2.08=-2.83 Z= (28.5-30.9)/2.08=-1.15
-2.83+-1.15=-3.98 50-3.98=46.02 46.02% score between 25 and 28.5)

c. How many children would we expect to find with scores between 28 and 31.5?(8 pts)
(What I came up With- Z=(28-30.9)/2.08=-1.39 Z=(31.5-30.9)/2.08=.28
-1.39+.28=-1.11 Z-Score=2.29,
X=30.9+2.08(2.29)= 35.66 36 Children have scores between 28 and 31.5)

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)
(What I came up With- . Z-Score=2.81 X=30.9+2.08(2.81)=9.74 Cut-Off is 9.74)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
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)
---
Find the z-score with a left tail of 30%::
invNorm(0.30) = -0.5244
Find the score using x = z*s + u
x = -0.5244*2.08+30.9 = 29.81
=======================================
(What I came up with- Z-Score=-2.75 X=30.9+2.08(-2.75)=25.18 Cut Off is 25.18)
Comment: You found the z-score with a left tail of 0.003.
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b. What percentage of children score between 25 and 28.5? (8 pts)
Z(25)= (25-30.9)/2.08=-2.83
Z(28.5)= (28.5-30.9)/2.08=-1.15
P(25< x < 28.5) = P(-2.83< z < -1.15) = normalcdf(-2.83,-1.15) = 0.1227
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c. How many children would we expect to find with scores between 28 and 31.5?(8 pts)
(What I came up With-
Z=(28-30.9)/2.08=-1.39
Z=(31.5-30.9)/2.08=.28
P(-1.39< z < 0.28) = normalcdf(-1.39,0.28) = 0.5280
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# of children = 0.5280*20 = 11 when rounded up
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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)
Find the z-score wit a left tail of 75%
invNorm(0.75) = 0.6745
---
Find the correspondig score:
x = z*s + u
x = 0.6745*2.08+30.9 = 32.3
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Cheers,
Stan H.
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