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The question reads:

"If \( X \) has a binomial distribution with \( p > 0.5 \), then the distribution of \( X \) is ______."

The options are:
a. Symmetric  
b. A normal distribution  
c. Skewed to the left  
d. Skewed to the right

### Explanation:

In a binomial distribution, \( p \) is the probability of success on a single trial. The shape of the distribution is influenced by \( p \):
- When \( p = 0.5 \), the distribution is symmetric.
- When \( p > 0.5 \), the distribution is **skewed to the left** (because more successes are expected, so the tail is on the left).
- When \( p < 0.5 \), the distribution is **skewed to the right**.

Given that \( p > 0.5 \), the correct answer is:

**c. Skewed to the left**

Would you like further details or have any other questions?

### Related Questions:
1. What happens to the binomial distribution when \( p = 0.5 \)?
2. How does increasing the number of trials (n) affect the shape of the binomial distribution?
3. What are the key properties of a binomial distribution?
4. How does a binomial distribution differ from a normal distribution?
5. What is the impact of skewness in practical applications of binomial distributions?

**Tip:** When \( n \) becomes large, the binomial distribution approximates a normal distribution regardless of skewness, as long as \( np \) and \( n(1-p) \) are sufficiently large.

If X has a binomial distribution with p > 0.5, then the distribution of X is ______.

Explore how the skewness of a binomial distribution is influenced by the probability parameter p. For p > 0.5, the distribution is skewed to the left. Learn about key concepts such as probability, binomial distribution formulas, and the implications of skewness in statistics.

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