## **Core Concept**
The infant mortality rate (IMR) is a measure of the number of deaths of infants under one year of age per 1000 live births in a given year. It is an important indicator of the health and well-being of a population. The IMR is calculated using the formula: (Number of deaths of infants under one year of age / Number of live births) * 1000.

## **Why the Correct Answer is Right**
To calculate the infant mortality rate, we first need to determine the number of live births and the number of infant deaths. Given that the birth rate is 30/1000 population and the population is 5000, the number of live births is 30/1000 * 5000 = 150. We are also given that 15 children died during the first year of life. Using the IMR formula: (15 / 150) * 1000 = 100.

## **Why Each Wrong Option is Incorrect**
- **Option A:** Without calculating, we cannot assume this is correct; let's verify other options.
- **Option B:** Similarly, we need to verify if this matches our calculation.
- **Option C:** This option suggests an IMR of 50, which would imply 7.5 deaths (since 7.5 / 150 * 1000 = 50), not matching our given data of 15 deaths.
- **Option D:** This option suggests an IMR of 100, which matches our calculation of (15 / 150) * 1000.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that the infant mortality rate is a sensitive indicator of the overall health and well-being of a population, including access to healthcare, nutrition, and environmental conditions. It is often used by healthcare professionals and policymakers to assess the quality of healthcare and to identify areas for improvement.

## **Correct Answer:** D. 100.