**Core Concept**
The normal distribution of a large dataset, such as the weights of 100 children, is described by the mean and standard deviation. In a normal distribution, about 68% of values lie within one standard deviation of the mean, and about 95% lie within two standard deviations.

**Why the Correct Answer is Right**
The correct answer is related to the empirical rule, which states that in a normal distribution:
- About 68% of values lie within 1 standard deviation (SD) of the mean (i.e., between mean - 1SD and mean + 1SD).
- About 95% of values lie within 2 standard deviations (SD) of the mean (i.e., between mean - 2SD and mean + 2SD).
- About 99.7% of values lie within 3 standard deviations (SD) of the mean (i.e., between mean - 3SD and mean + 3SD).
In this case, since the mean weight is 15 kg and the standard deviation is 1.5 kg, we can calculate the range within which 95% of the children's weights lie.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incomplete and cannot be evaluated.
* **Option B:** There is no information provided to support this statement, and it is not a direct consequence of the given data.
* **Option C:** This option is incorrect because it does not follow from the given data. The 5th percentile is not directly calculable from the information provided.
* **Option D:** This option is incorrect because it does not follow from the given data. The 95th percentile is not directly calculable from the information provided.

**Clinical Pearl / High-Yield Fact**
It's essential to remember the empirical rule for normal distributions, which helps in understanding the spread of data and making predictions about the range of values within which most data points lie.

**Correct Answer:** C.