Questions: X is the weight in pounds of a newborn elephant, and X̄ is the sample mean of the 50 baby elephants.

Solution Steps

Let \( X \) be the weight in pounds of a newborn elephant, and let \( \bar{X} \) be the sample mean of the weights of the 50 baby elephants.

To calculate the margin of error for the mean weight of newborn elephant calves at a \( 95\% \) confidence level, we use the formula:

\[ \text{Margin of Error} = Z \cdot \frac{\sigma}{\sqrt{n}} \]

Where:

• \( Z = 1.96 \) (Z-score for \( 95\% \) confidence)
• \( \sigma = 15 \) (population standard deviation)
• \( n = 50 \) (sample size)

Substituting the values:

\[ \text{Margin of Error} = 1.96 \cdot \frac{15}{\sqrt{50}} \approx 4.1577 \]

The confidence interval for the mean is given by:

\[ \bar{x} \pm Z \cdot \frac{\sigma}{\sqrt{n}} \]

Substituting the known values:

\[ 244 \pm 1.96 \cdot \frac{15}{\sqrt{50}} \implies (244 - 4.1577, 244 + 4.1577) \implies (239.84, 248.16) \]

Final Answer