Reference no: EM133616869

Question: A normal distribution is a pattern that often occurs in nature when you measure something, like heights or test scores, and it helps us understand how most values cluster around an average with some variability (OpenAI., 2023a). The Student t-distribution is a way to handle the uncertainty of smaller samples when we're trying to make predictions about a larger group (OpenAI., 2023b). The empirical rule helps us understand how data spreads in a normal distribution. It's a way to make quick estimations about the distribution of values without examining each data point. (OpenAI., 2023c). A. Why is it essential to collect a random sample when conducting inferential statistics? ZyBooks 2.1 B. Explain the practical application of the central limit theorem (CLT). How does the CLT change the value of the standard deviation, s, when applied? ZyBooks 3.4 C. When is it appropriate to use the Student t-distribution instead of the standard normal distribution? (What are the two conditions?) ZyBooks 3.5 D. Empirical Rule ZyBooks 3.6 a. What are the advantages of using the empirical rule? b. Suppose a population of animals in a zoo has an average lifespan of 13.1 years with a standard deviation of 1.5 years and follows a normal distribution. Manually calculate the likelihood or chance of an animal living beyond 16.1 years (Hayes et al., 2023). E. Describe where you can collect data and where the empirical rule applies. How does knowing that information help?