IQ level 110, approximately 95% distribution is?

NORCET -4 , 2023

Nursing Research & Statistics

Hard

Appeared in: NORCET -4 , 2023

Explanation

IQ scores are modeled on a normal distribution (bell curve) with a mean of 100 and a standard deviation (SD) of 15.
The 68-95-99.7 rule states that approximately 95% of the population falls within two standard deviations of the mean.
Calculating this range: 100 ± (2 × 15) gives an IQ range of 70 to 130.
Among the given options, the range 80-130 is the closest approximation to the correct statistical range of 70-130.

Option B: The range 100-120 is too narrow. It represents scores from the mean to just over one standard deviation above the mean, covering a much smaller percentage of the population than 95%.
Option C: The upper limit of 220 is extremely unrealistic. The vast majority of the population (99.7%) scores below 145. Scores above 200 are exceptionally rare and not used for standard population distributions.
Option D: The range 90-110 is defined as the 'Average' range. It covers approximately 50% of the population, not 95%. This range is roughly within two-thirds of a standard deviation from the mean.

Visual 1: Diagram - A bell curve illustrating the normal distribution of IQ scores. The x-axis should be marked with IQ scores (70, 85, 100, 115, 130), and the areas under the curve should be shaded and labeled with percentages (68%, 95%, 99.7%) corresponding to 1, 2, and 3 standard deviations.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Normal distribution of IQ scores and the empirical rule (68-95-99.7) as background academic context rather than a clinical decision trigger.
Nurses can use their understanding of IQ levels to assess a patient's ability to comprehend complex health information, consent for procedures, and adhere to treatment plans.
This knowledge is crucial in psychiatric and pediatric nursing for creating appropriate care plans and educational materials for patients with varying cognitive abilities.
What if the question asked for the range covering 68% of the population? The answer would be 85-115 (100 ± 15), which represents one standard deviation from the mean.

How to Approach the Question

First, identify the key terms in the question: 'IQ' and '95% distribution'. The number '110' is likely extraneous information intended to distract.
Recall the standard properties of IQ score distribution: it follows a normal (bell) curve with a mean of 100 and a standard deviation of 15.
Apply the '68-95-99.7' empirical rule. The question asks for the 95% distribution, which corresponds to the range within two standard deviations (2 SD) of the mean.
Calculate the range: Mean ± 2 SD = 100 ± (2 × 15) = 100 ± 30, which equals 70 to 130.
Compare the calculated correct range (70-130) with the given options.
Select the option that is the closest match. In this case, 80-130 is the best fit among the choices provided.

Concept Tested & Keywords

Concept Tested: Normal distribution of IQ scores and the empirical rule (68-95-99.7).
Stem keywords: IQ level, 95% distribution
Lead-in keywords: is
Clinical cues: The phrase '95% distribution' is a direct cue to apply the empirical rule for normal distributions, specifically the part corresponding to two standard deviations from the mean.

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