Normal Curve and Statistical Criteria in Medical and Educational Testing

Use of the Normal Curve in Determining Normal Ranges

(1). Statistical criteria are sometimes used for determining what is "normal" for the population. Often, when responses are normally distributed, the normal curve is used to determine the range of normal (and abnormal) responses. This is one reason why the curve is called the "normal" curve. Normal curve criteria are used for determining normal ranges for both medical testing and educational testing. 

A good example of the use of curve in this way is in determining educational programs for children. Children are often categorized and assigned to special education programs based at least in part on their IQ scores. For example, an IQ of less than 70 (2sd's below the mean) is one of the criteria for labeling a child as 'mentally retarded. 

Do you think this use of the normal curve is appropriate? Should we be applying statistical criteria in diagnosis?   Should statistical criteria be used deciding appropriate educational programming? Give relevant examples to support your answer.

(2). A medical aptitude test has been administered over a period of years to 8000 senior premedical students from a large number of US colleges and universities. The frequency distribution of scores very closely approximates the normal curve and has a mean of 90 and a standard deviation of 16. Using this information, answer the following questions:

Another medical college accepts either this medical aptitude test score or a GRE for admission. They routinely convert the medical school aptitude test scores to equivalent GRE scores (mean = 500 and standard deviation = 100), What would be the GRE equivalent for a raw score of 120?

(3). Scores on Wechsler Adult Intelligence Scale (WAIS) approximate a normal curve with a mean of 100 and a standard deviation of 15. What proportion of IQ scores are 

(a)    above Kristen’s 125 ?
(b)    below 82?
(c)    Within 9 point of the mean?
(d)    More than 40 points from the mean?