Suppose that the amount of time the Australian high school students spend on doing sports weekly is normally distributed with a standard deviation of 40 minutes. A random sample of 15 high school students was drawn. Each reported the amount of time spent on sports (in minutes) are listed below. Determine the 95% confidence interval estimate of the population mean. 130 120 60 200 180 80 240 210 150 125# 180 130 150 165 90According to research, the average number of working hours of young academic researchers perweelc inAustralia is 45.4 hours and the standard deviation is 3.3 hours. Suppose arandom sample of 36 young academic researchers is taken. \" i) 1What is the probability that the sample mean is more than 4? hours? (4 marks)\" ii) What is the probability that the sample mean is loss than 43 .5 hours? (4 marks)\" iii) What is the probability that the sample mean is less than 42 hours? (4 marks)\" 44 The owner of a swimming course is concerned about slow pay, which clogs the course and results in selling fewer rounds. She believes the problem lies in the amount of time taken to sink putts on the green. To investigate the problem, she randomly samples 10 groups and measures the amount of time they spend on the 18th green. The data are listed below. Assuming that the times are normally distributed with a standard deviation of 2.5 minutes, test to determine whether the owner can infer at the 10% significance level that the mean amount of time spent put on the 18" green is greater than 6 minutes. ~ 10 6 7 6 7