math
posted by Sasha on .
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 cutoff score for these children?
B) What percentage of children score between 25 and 28.5?
C) How many children would we expect to find with scores between 28 and 31.5?
D) Children in the top 25% are considered accelerated readers and qualify for different placements in school. What raw score would mark the cutoff for such placement?
#2. Age at onset of dementia was determined for a sample of adults between the ages of 60 and 75. For 15 subjects, the results were EX=1008, and E(XM)^2 = 140.4. Use this information to answer the following:
A) What is the mean and SD for this data?
B) Based on the data you have and the Normal Curve Tables, what percentage of people might start to show signs of dementia at or before age 62?
C) If we consider the normal range of onset in this population to be +/1 zscore from the mean, what two ages correspond to this?
D) A neuropsychologist is interested only in studying the most deviant portion of this population, that is, those individuals who fall within the top 10% and the bottom 10% of the distribution. She must determine the ages that mark these boundaries. What are these ages?

#1. Z = (scoremean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions that correspond to the Z scores. For D, reverse process and insert Z score in equation above.
#2. A) Assuming EX = mean of sample, divide E(XM)^2 by the number of scores to get variance.
Standard deviation = square root of variance
B, C, D) Use the table and equation above.
I'll let you do the calculations. 
67.2 = mean
10.03= SD
percentage=48.81%