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 ($) in the previous trip were...

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 ($) in the previous trip were recorded as follow:
8200 8500 4300 5200 5600 7800 2310 10000
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?