STA2300 Data Analysis - Tutoring 1

Question 6 (18 marks)
The COVID-19 virus has become a real threat to many human lives. It is particularly life threatening to people over the age of 70 years. Research has shown that this virus kills 15% of COVID-19 infected people over the age of 70 years in nursing homes. To study the number of deaths among the COVID-19 infected people over the age of 70 years, an epidemiologist selects a random sample of 20 residents of age over 70 years who are infected with COVID-19 from nursing homes.

Based on the above information answer the following questions:

1. (1 mark) What is the variable of interest here?
2. (3 marks) What is an appropriate model to represent the distribution of the variable of interest? Identify the parameters of the model and state the values of these parameters in this context.
3. (4 marks) Discuss how the conditions of the appropriate model are satisfied in the current study. Explain the conditions in the context of the problem.
4. (2 marks) Find the mean and standard deviation of the variable using the parameters of the model.
5. (3 marks) Find the probability that less than 3 of the 20 randomly selected over 70 years residents infected with COVID-19 will die.
6. (5 marks) In a random sample of 150 residents of age over 70 years who are infected with COVID-19 from the nursing homes, determine the probability that 30 or more will die. State and check relevant assumptions, conditions or rules of thumb that should be considered before performing the calculations to determine this probability.