Question: please provide workout solutions for these 2 questions the...
Please provide workout + solutions for these 2 questions. The homework is due in one day and have no idea how to do it :(
A polling company performed research on how well Australian state premiers were performing in light of the COVID-19 pandemic. Respondents form each state of Australia were asked for their level of approval for their particular state premier, with possible option of “approve”, “don’t know”, and “disapprove”. In addition to this their gender was recorded.
Among men, 40 approved, 45 disapproved and 10 said don’t know.
Among women, 62 approved, 30 disapproved and 5 said don’t know.
For the following questions, use A1 to define the event that someone approves of their state premier, A2 and A3 to define the events disapproved and don’t know respectively. Let the event M represent the event that the respondent was male. Use the above sample counts to determine the probabilities asked for in the following questions.
(a) What type of variable is the level of approval for one’s state premier? Carefully
explain your reasoning.
(b) Construct a contingency table summarising the data collected.
(c) If we were to choose a male at random, what is the probability that they will
approve of the state Premier’s performance?
(d) What is the probability that a randomly selected Australian is a woman who
approves of the state Premier’s performance?
(e) What is the probability that a randomly selected Australian approves of their
A German physician, Carl Wunderlich, measured temperatures from about 25,000 people in the mid 1800s and found that the average was 37 degrees Celsius. There is some evidence that the mean body temperature has been changing over time.
Assume that the body temperature of adults is approximately normally distributed with a mean of 37 degrees Celsius and standard deviation 0.40 degrees Celsius.
(a) What value of body temperature distinguishes the highest 10%?
(b) People with body temperatures above 38 degrees are said to have a significant fever.
Show that approximately 0.62% of people have a significant fever.
(c) Suppose we take a random sample of 50 people and want to determine whether or not they have a significant fever. Let X represent the number of people in a sample of size 50 who have a significant fever. What probability distribution does X follow? Justify your answer.
(d) Using the probability distribution from part (c), find the probability that at least 1 person in the random sample of 50 have a significant fever.