Matching Normal Curve Concepts

This question requires matching specific statistical scenarios (SAT scores, Binet scale, standard deviation values) with their corresponding properties related to the normal curve, specifically its total area and mean ($\overline{X}$). A systematic analysis of each item in LIST-I helps establish the correct pairings.

Key Normal Curve Properties

• Total Area: The total area under any normal probability distribution curve is always equal to 1. This represents the entire probability space.
• Standard Normal Distribution (Z-distribution): This is a special case where the mean ($\overline{X}$) is 0 and the standard deviation ($\sigma$) is 1.
• Standardized Scores: Many standardized tests are designed to have a specific mean and standard deviation.

Matching LIST-I with LIST-II

Let's analyze each item:

• A. SAT score $\sigma = 100$: SAT scores are typically standardized with a mean ($\overline{X}$) around 500 and a standard deviation ($\sigma$) of 100. Therefore, A matches with $\overline{X} = 500$.
• B. Total area: As a fundamental property of probability distributions, the total area under the normal curve is always 1. Therefore, B matches with 'equal to 1'.
• C. In a distribution if $\sigma$ is 1: A standard deviation of 1, often paired with a mean of 0, defines the standard normal (Z) distribution. Therefore, C matches with $\overline{X} = 0$.
• D. In Binet intelligence scale score $\sigma = 16$: The Binet scale (and other IQ tests) is commonly standardized to have a mean ($\overline{X}$) of 100, with a standard deviation ($\sigma$) typically around 15 or 16. Therefore, D matches with $\overline{X} = 100$.

Based on this analysis, the correct matching is:

• A matches with IV ($\overline{X} = 500$)
• B matches with I (equal to 1)
• C matches with II ($\overline{X} = 0$)
• D matches with III ($\overline{X} = 100$)

This corresponds to the combination A-IV, B-I, C-II, D-III.