In a study of monthly salary distribution of residents in Parisconducted in year 2015, it was found that the salaries had anaverage of €2200 (EURO) and a standard deviation of €550. Assumethat the salaries were normally distributed.

Question 1: Consider sampling with sample size 64 on the abovepopulation. Compute the mean of the sampling distribution of themean (?Ì…).

Question 2: Compute the standard deviation of the samplingdistribution of the mean in Question 1 above.

Question 3: A random sample of 64 salaries (sample 1) wasselected from the above population. What is the probability thatthe average of the selected salaries is above €2330?

Question 4: Would the calculation you performed in Question 3still be valid if the monthly salaries were NOT normallydistributed? Why? In another study conducted in the same year(2015), the average monthly salary of residents in Bordeaux wasfound to be about €2353. And the standard deviation of the monthlysalaries was €420. A random sample of 81 salaries (sample 2) wasselected from this population. Set 1 = Paris (2015); 2 = Bordeaux(2015)

Question 5: Compute the mean of ?̅ 1 − ?̅ 2.

Question 6: Compute the standard deviation of ?̅ 1 − ?̅ 2.

Question 7: What is the probability that the average of thesalaries in the sample 1 is less than the average of the salariesin sample 2? In 2017, a study on the salary distribution of Parisresidents was conducted. Assume that the salaries were normallydistributed. A random sample of 10 salaries was selected and thedata are listed below: 3200 3500 3000 2100 2950 2050 2440 3100 35002500

Question 8: Assume that the standard deviation of the salarieswas still the same as in 2015. Estimate the average salary (in2017) with 95% confidence.

Question 9: The assumption made in Question 8 was certainlyunrealistic. Estimate the average salary (in 2017) with 95%confidence again assuming that the standard deviation had changedfrom 2015.

Question 10: Estimate the variance of monthly salaries of Parisresidents (in 2017) based on the sample provided above at a 95%confidence level.

Question 11: How would you interpret the result in Question 10above? A similar study was conducted on salary distribution ofParis residents in 2019. The research team aimed to estimate theaverage salary. They chose the 98% confidence and assumed that thepopulation standard deviation was the same as in 2015. Assume againthat those salaries were normally distributed.

Question 12: If they would like the (margin of) error to be nomore than €60, how large a sample would they need to select?