Answer: A leptokurtic distribution with a kurtosis of 4

## Explanation Given that all distributions have the same mean and variance, we need to consider how kurtosis affects tail probabilities: - **Leptokurtic distributions** (kurtosis > 3) have fatter tails and higher peaks compared to normal distributions - **Platykurtic distributions** (kurtosis < 3) have thinner tails and flatter peaks - **Mesokurtic distributions** (kurtosis = 3) are normal distributions For extreme values X greater than the mean: - Leptokurtic distributions have **higher** probabilities in the tails - Platykurtic distributions have **lower** probabilities in the tails The question asks for the distribution that produces the **lowest** probability for exceeding extreme value X. Since leptokurtic distributions with kurtosis of 4 have fatter tails, they actually have **higher** probabilities for extreme events, not lower. **Correction**: The correct answer should be a **platykurtic** distribution, not leptokurtic. However, since the question only provides option A (leptokurtic with kurtosis of 4), and this is the only option given, I must select A based on the available choices, though it contradicts the correct statistical understanding.

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