Full marks: 30 marks Show your calculation steps clearly. Correct you answer to 4 decimal places and report the measurement unit when applicable. Question 1 (10 marks) A surveying company wants to know the average amount of people spent in a trip. A random sample of 8 people was taken and their amount of spendings (S) in the previous trip were recorded as follow: 2310 10000 8200 8500 4300 5200 5600 7800 It is assumed that the amount spent was normally distributed. (a) Construct a 95% confidence interval of the population mean spending in a trip. = (b) If the similar survey would be done regularly, each time with the same sample size n = 8. After the construction of 50 confidence intervals, each at 95% confidence level, approximately how many such intervals can successfully include the unknown population mean