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.