Final answer:
Statistical questions are A and C, which seek data analysis due to variability in elephants' weights and lifespans. Question B is not statistical as it seeks a specific number. A confidence interval for elephant calf weights utilizes the normal distribution and sample statistics provided.
Step-by-step explanation:
To determine which of the given questions are statistical questions, we look for queries that anticipate variability in the data and require data analysis to answer. Here are the questions:
- How heavy are elephants?
- How many elephants does the Smithsonian's National Zoo have?
- How long does a typical elephant live?
Question A asks about the weight of elephants. Since the standard deviation of elephant weights is given later in a reference and a mean weight can be computed by collecting data, this qualifies as a statistical question because it expects variation and seeks a summary measure.
Question B is not a statistical question because it asks for a specific, singular fact that does not vary.
Question C is a statistical question as it asks about the typical lifespan of an elephant, which implies the need for data on various elephants' lifespans and would involve analysis such as calculating the mean lifespan.
When constructing a confidence interval for the mean weight of newborn elephant calves, given a standard deviation of 15 lb and a sample standard deviation of 11 lb, the normal distribution could be used due to the sample size of 50, which by the Central Limit Theorem, allows us to approximate the distribution of the sample mean as normal.
Creating a 95% Confidence Interval
- Identify the sample mean (244 lb).
- Use the sample standard deviation (11 lb) as an estimate of the population standard deviation.
- Apply the normal distribution to calculate the error bound with a 95% confidence level.
- Finally, construct the interval using the sample mean and the error bound.