<p>For a normal distribution if the mean is \(M\), mode is \(M_0\) and median is \(M_d\), then</p>
Step-by-Step Solution
Key Concept: In a normal distribution, the mean, median, and mode are all equal due to the symmetric bell curve around the center. This fundamental property holds for any normal distribution regardless of parameters.
<p><strong>Key Property of Normal Distribution:</strong> A normal distribution is perfectly symmetric about its center.</p><p><strong>Step 1:</strong> By definition, the mode is the point of maximum frequency. In a normal distribution, this occurs at the center of symmetry.</p><p><strong>Step 2:</strong> The median divides the distribution into two equal halves. Due to perfect symmetry, the median also lies at the center.</p><p><strong>Step 3:</strong> The mean (average) of a symmetric distribution is also located at its center of symmetry.</p><p><strong>Step 4:</strong> Since all three measures locate at the same central point for a normal distribution:</p><p><strong>M = M₀ = M_d</strong></p><p>∴ Answer: D (assuming option D states M = M₀ = M_d)</p>
Correct Answer: D