HAP 719: Advanced Statistics I 

Distributions
OverviewThis module provides an understanding of normal distributions, enabling students to describe their key characteristics and estimate the probability of events using the standard normal curve. Additionally, the module covers techniques for transforming nonnormal distributions into normal distributions to facilitate statistical analysis. Learning Objectives
Lectureindicates AI assisted material.
AssignmentsAssignments are submitted on blackboard. They are graded as pass/fail. A summary 1page word document should be included. In the summary, you should state if you were able to get the same answers as those provided. Your R, STATA, or Python code should be included in separate files. No late assignments are accepted. It is OK to help each other in doing the assignments but not OK to copy and paste work of others. It is OK to use ChatGPT or other large language models to generate the R code, but you must be transparent about it and report its use. Question 1: A particular health related test has a mean score of 500 and a standard deviation of 100. In a sample of 30 students the mean test score was 525 and standard deviation was 75. (a) Test that the sample comes from the population. (b) draw the two distributions. (c) Provide a confidence interval for the mean of the sample. Resources for Question 1:
Question 2: Assume that the average length of stay for individuals having cardiac bypass surgery is normally distributed with a mean of 9 days and a standard deviation of 1.25 days. What is the probability that a bypass patient will have length of stay of 8 days. Resources for Question 2:
Question 3: Calculate the probability of the following events for a distribution with mean 10 and standard deviation 5.
Resources for Question 3:
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