Prof Rea’s Exam Q8 The distribution of heights of US female college students is approximately normal with a mean of 63.5 inches and a standard deviation of 2.8 inches. Janet, a female college student, has a height with a Z-score of -1.58 when her height is compared to all US female college students. Write a sentence to interpret the meaning of the Z-score. Then compute Janet’s height, measured in inches. Use the empirical rule to find the proportion of US female college students that are shorter than 66.3 inches. Show your thinking on the graph by labeling the horizontal axis with the appropriate heights, labeling the regions of the graph with the appropriate areas, and shading the appropriate area.

For a particular disease at a specific time period, morbidity rates should always be equal or greater than mortality rates.

If a prodromal period exists for a certain disease, it should occur prior to ____________.

Prof Rea’s Exam Q7 A survey finds that 22% of all healthcare workers in the US refuse to get the COVID-19 vaccination. (The population is large enough for trials to be considered independent). What is the probability that a randomly selected healthcare worker in the US will not refuse the COVID-19 vaccination? What is the probability that all 3 randomly selected healthcare worker in the US refuse the COVID-19 vaccination? Round your answer to three decimal places. What is the probability that of 15 randomly selected healthcare worker in the US, exactly 3 refuse to get the COVID-19 vaccination? Use binomial probability. Round your answer to three decimal places. Show the calculation to earn full credit.

Prof Rea’s Exam Q11 Given below is a clickable scatterplot that shows the number of non-commercial space launches worldwide and the number of Sociology doctorates awarded in the US.    Sample mean  Sample standard deviation Linear correlation coefficient  Worldwide non-commercial space launches (x) 44.846 5.273 0.789 Sociology doctorates awarded (y) 585.769 32.231   Based on the linear correlation coefficient 0.789, what is the strength and direction of this scatterplot? Explain.  Compute and interpret the slope of the line of best fit in context. Round to two decimal places.  Compute and interpret the y-intercept of the line of best fit in context. Round to two decimal places.  Write the equation of the line of best fit. Use the equation to find the residual for the year 1997 when there were 54 launches and 601 degrees awarded. Based on this scatterplot, do you believe that an increase in worldwide non-commercial space launches will cause the number of sociology doctorates awarded to increase? Explain. 

Prof Rea’s Exam Q6 A statistician wanted to examine the proportions of various racial groups that are incarcerated in California. She collects data from a random sample of 256 Californian’s that have been arrested and charged with a crime. The following table shows this sample organized into the categories of race, and whether they are incarcerated or not.  White Black Other Total Incarcerated 12 54 27 159 Not Incarcerated 64 34 65 97 Total 76 88 92 256 Calculate the probability that a randomly selected individual from the sample is black. Use probability notation and write your answer as a fraction and decimal rounded to three decimal places. Calculate the probability that a randomly selected individual from the sample is black and incarcerated. Use probability notation and write your answer as a fraction and decimal rounded to three decimal places. Are white individuals, black individuals, or individuals with other race more likely to be incarcerated? Explain and show each calculation with proper probability notation to earn full credit. 

Prof Rea’s Exam Q3 A researcher conducted a study to determine if an antidepressant reduces the chance of migraines. He randomly assigned 300 patients to take the antidepressant every day and 300 patients to take a placebo every day. After a certain length of time, he reported the number of migraine days in the patients who took the antidepressant every day and in those who did not take the antidepressant every day. Identify the explanatory and response variables.

Exam Question 6 A student completes the following question incorrectly. Explain the mistake they made, and fix the mistake:  Question: Consider the following two distributions:  The time doctoral students spend studying for their midterm exam. The time high school students spend studying for their midterm exam.  Which of these distributions would have a larger standard deviation? Explain your answer. Answer: I believe that time doctoral students spend studying for a midterm exam has a higher standard deviation because their midterm will be harder, and therefore they will study longer than high school students.

Exam Question 7 The following table shows the number of people who developed Covid-19 in a sample of 94 total participants who developed Covid-19. Participants are organized by their reported gender and whether they received a vaccine or placebo in the trial.  Vaccine Placebo Total Male 4 42 46 Female 3 36 39 Other 1 8 9 Total 8 86 94 What is the probability of someone with a placebo developing Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places.  What is the probability that someone who is female and takes a placebo develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places. Given a subject is female, what is the probability that someone who takes a placebo develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places. A student answers the following question incorrectly. Explain the mistake they made and answer the question correctly (use proper notation and justify your answer with a calculation).  Question: Is it more likely to meet a man with a placebo that developed Covid-19 or a woman with a placebo that develops Covid-19? Answer: Since there are more men who received the placebo than women, you are more likely to meet a man with a placebo that developed Covid-19. What is the probability that someone who is female or takes a placebo develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places.

Prof Rea’s Exam Q6 A statistician wanted to examine the proportions of various racial groups that are incarcerated in California. She collects data from a random sample of 256 Californian’s that have been arrested and charged with a crime. The following table shows this sample organized into the categories of race, and whether they are incarcerated or not.  White Black Other Total Incarcerated 12 54 27 159 Not Incarcerated 64 34 65 97 Total 76 88 92 256 Calculate the probability that a randomly selected individual from the sample is white. Use probability notation and write your answer as a fraction and decimal rounded to three decimal places. Calculate the probability that a randomly selected individual from the sample is white and incarcerated. Use probability notation and write your answer as a fraction and decimal rounded to three decimal places. Are white individuals, black individuals, or individuals with other race more likely to be incarcerated? Explain and show each calculation with proper probability notation to earn full credit.