A function reaches its maximum value at_______________?
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Answer: B. X = µ
Explanation
The normal distribution curve is completely symmetrical around its very center. This mathematical symmetry ensures that the mean, median, and mode coincide perfectly. Therefore the highest point of the bell-shaped curve always occurs at the mean. The normal distribution is a fundamental continuous probability distribution in statistics. It is fully defined by two parameters which are the mean and variance. The parameter mu represents the population mean and sigma denotes the standard deviation.
Many natural phenomena such as human heights and test scores follow this curve. Researchers rely on this property to identify the most typical value in a dataset. Understanding the peak helps analysts determine the central tendency of measured variables. Option A suggests the peak occurs at the variance which is incorrect mathematically. Option C adds the standard deviation moving away from the central peak location. Option D places the maximum value at zero which only happens in specific standardized cases.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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