Part 1

1. What percentage of observations from a standard normal distribution are below a z-value of -2.15?
2. What percentage of observations from a standard normal distribution are above a z value of -2.15?
3. What percentage of observations from a standard normal distribution are above a z value of 2.15?
4. What percent of observations from a standard normal distribution are between -2.15 and 2.15?
5. Based on your answers to the above questions, list two facts that you notice about the standard normal distribution. (Please write your answer in complete sentences.)
Part 2
1. The Central Limit Theorem is probably the most important theorem we will learn about in statistics. What is the purpose of the Central Limit Theorem in your own words. Find an example from the internet that uses/discusses the use or application of the CLT. Be sure to give the link and a brief summary of the example. What happens to the z-value and probability as the sample size for the CLT gets larger?
Part 3
Suppose you administer a certain aptitude test to a random sample of 9 students in your high school, and the average score is 105. We want to determine the mean μ of the population of all students in the school. Assume a standard deviation of σ = 15 for the test. Round all answers to 2 decimals.
2. What is the margin of error for a 98% confidence interval?
3. What would be the interval for a 98% confidence interval?
4. Write a sentence explaining the 98% confidence interval in context of the question. (There are only a few ways to do this correctly, so be sure to read the book closely.)
5. Write a few sentences explaining what would happen if you wanted a 80% confidence interval?
6. Write a few sentences explaining what would happen if you changed the sample size to be 81 and kept a 98% confidence interval.
Part 4
For a group of 10 men subjected to a stress situation, the mean number of heartbeats per minute was 126 and the sample standard deviation was 4. Round all answers to 2 decimals.

1. What is the margin of error for a 95% confidence interval?
2. What is the 95% confidence interval of the true mean?
3. Write a sentence explaining the 95% confidence interval in context of the question. (There are only a few ways to do this correctly, so be sure to read the book closely.)
4. Write a few sentences explaining what would happen if you wanted a 90% confidence interval?
5. Write a few sentences explaining what would happen if you changed the sample size to be 1000 men and kept a 95% confidence interval.