Question 4 (25 marks) (i) (9 marks) Due to the aftermath of Covid-19 pandemic, global turmoil, and tough job market, Sara is working two casual jobs, as a kitchen hand and a care giver. Average hourly pay for a kitchen hand is $20, with a standard deviation of $5. Average hourly pay for a care giver is $30 with a standard deviation of $6. Assume that the salaries in these two jobs are normally distributed. a) What are the probabilities that Sara will earn at least $15 in jobs of kitchen hand and $25 for care giver? (3 marks) b) What is the probability that Sara's hourly pay is between $28 and $33 for care giver job? (3 marks) c) How high does an hourly rate have to be to put Sara in the top 5%% high earning workers in both jobs? (3 marks) (ii) (16 marks) AQ stands for analytical quotient and describes a score earned on a test designed to measure analytical knowledge. Students at a University in Parkville have AQ scores assumed to be normally distributed with a mean of 100 and a standard deviation of 15. We would like to find the answers to the following questions. a) Find the probability that a student selected at random has an AQ score of more than 92. (3 marks) b) Find the probability that a student selected at random has an AQ score between 80 and 110. (4 marks) c) Find the highest possible AQ score so that it is amongst the lowest 20%% of all scores. Round your answer to the nearest integer that would be within the lowest 20% of all AQ scores. (4 marks) d) The probability that a randomly selected student has an AQ score of at least 100 + K is 0.3264. Find, to the nearest integer, the value of K