Final answer:
The random variable X is the weight of an individual newborn elephant, and X is the sample mean of newborn elephant weights for a sample size of 50. The normal distribution should be used in constructing a confidence interval for the mean weight as the central limit theorem applies.
Step-by-step explanation:
The question is asking for the definitions of the random variables X and X as they pertain to a statistical exercise involving the construction of a confidence interval for the mean weight of newborn elephant calves.
The correct answer to the question of defining the random variables would be: B. X is the weight in pounds of a newborn elephant, and X is the average of weights of the sample of 50 baby elephants. Here, X represents an individual measurement of newborn elephant weight, while X symbolizes the sample mean weight of the group of fifty newborn elephant calves. This nomenclature helps differentiate between individual data points and aggregate statistics derived from those points.
As for the distribution to be used, it would be normal due to the large sample size and the fact that the population standard deviation is known. The assumption of normality is justified based on the central limit theorem, which states that the distribution of sample means approaches a normal distribution as the size of the sample increases, even if the population distribution itself is not normally distributed.