IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. According to the Wechsler IQ testing agency, a person with an IQ of 40 or below is an Idiot. What proportion of IQ test takers are not Idiots?
Question:
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. According to the Wechsler IQ testing agency, a person with an IQ of 40 or below is an Idiot. What proportion of IQ test takers are not Idiots?
Answers (1)
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Answers (1)
FayApril 16, 2023 в 07:07
The first step in solving this problem is to standardize the IQ score using the formula:
z = (X - mu) / sigma
where z is the standardized score, X is the IQ score, mu is the mean, and sigma is the standard deviation.
For an IQ of 40 or below:
z = (40 - 100) / 15 = -4
To find the proportion of IQ test takers who are not Idiots, we need to find the area under the normal curve to the right of this z-score. We can use a table or calculator to find this area, which is \approx imately 1.00.
Therefore, the proportion of IQ test takers who are not Idiots is 1.00 or 100%.
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