Final answer:
The question involves the application of statistics within mathematics to understand the normal distribution, specifically concerning the lifespan of zebras and other examples. It covers aspects such as standard deviations, random variables, types of hypothesis tests, and testing of means or proportions.
Step-by-step explanation:
The question pertains to the concept of normal distribution in statistics, a topic covered in mathematics. Specifically, the question asks about the lifespan of zebras in a zoo, which is said to follow a normal distribution with a known mean. However, the standard deviation is not provided in the question. According to the question, we need to address the elements highlighted in the given information. Assuming there is an error and the standard deviation is indeed provided, we could then proceed in our explanation.
Standard Deviations
In the context given, the standard deviations are known for the populations discussed, such as the tire's lifespan and the weights of elephants and marathon runners. Standard deviation is a measure of variability that quantifies the amount of dispersion in a set of values.
Random Variable
The random variable would be the specific measure being studied, such as the lifespan of a zebra or the length of time a worker stays with a company. This variable can take on different values based on the outcome of random phenomena.
One-Tailed or Two-Tailed Test
Whether a test is one-tailed or two-tailed depends on the alternative hypothesis. A one-tailed test examines if a value is greater than or less than some number, while a two-tailed test checks if a value is significantly different from some number in either direction.
Test of Means or Proportions
The example regarding life expectancy in a county for whites and nonwhites would be a test of means. This test checks whether the average results are significantly different between two groups.