According to a study carried out by the firm Optima Groupe Conseil for the newspaper Les Affaires, the average income per household in the Trois-Rivieres-Ouest geographic area is $ 55,577 (this value was obtained from the Statistics Canada database - 2001 census). Let us assume that the standard deviation of the income per household is $ 4,000.

A random sample of 64 households in this geographic area is collected.

• a. What are the parameters of the sampling distribution of the variable "average income per household" for a sample of size n = 64? (1 point)
• b. What assumptions and conditions are required to answer c) and d)? (1 point)
• c. What is the probability that the average income in the sample per household in the Trois- Rivieres-Ouest geographic area will be less than $ 54,777? (2 points)
• d. What is the probability that the average income in the sample per household in the Trois- Rivieres-Ouest geographic area is between $ 54,327 and $ 56,827? (2 points)