If the mean and the median pertaining to a certain character of a population are of the same value, the following is most likely to occur:-

Options

A. A skewed curve
B. A normal distribution
C. A bi-modal distribution
D. a T-shaped curve

Answer

To solve the question regarding the relationship between the mean and median of a population's character, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mean and Median**:
- The mean is the average of a set of values, calculated by summing all values and dividing by the number of values.
- The median is the middle value when the values are arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.

2. **Analyzing Distribution Types**:
- **Normal Distribution**: This is a symmetric distribution where the mean, median, and mode are all equal. It is often represented as a bell-shaped curve.
- **Skewed Distribution**: In a skewed distribution, the mean and median are not equal. The mean is pulled in the direction of the skew (left or right).
- **Bimodal Distribution**: This distribution has two different modes (peaks). The mean and median can differ significantly in this case.
- **T-Shaped Curve**: This is an inverted distribution where the mean and median are generally not equal.

3. **Identifying the Correct Distribution**:
- Since the question states that the mean and median are of the same value, we can eliminate skewed, bimodal, and t-shaped distributions as they do not satisfy this condition.
- The only distribution where the mean and median are equal is the normal distribution.

4. **Conclusion**:
- Therefore, if the mean and median of a certain character of a population are the same, the distribution is most likely a **normal distribution**.

### Final Answer:
The correct answer is **normal distribution**.

---