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) Question: Place the 9 dots in the maps 1, 2, and 3 below based on the methods of dot placement: uniform, geographically weighted, and geographically based. Show values in each dot. Hint: The values inside the dots will be useful to answer for the map, "2. Geographically weighted". Use the "Ancillary information" map below to answer for the map, "3. Geographically based". The Ancillary information map tells that the phenomena are generally occurred in the area B rather than the area A. 10 (32) B A Original observations Ancillary information 1. Uniform 2. Geographically weighted 3. Geographically based 1. i. ii. iii. iv. V. General questions on probability and statistics: The probability of a flood occurring every year is 0.4. What is the probability of this event occurring in year 2 but not in year 1? What is the probability that a 5-year flood event will occur four times in a 10-year period? What is the probability that a 5-year flood will occur less than four times in a period of 10-years? What is the probability that a 5-year flood will not occur at all in a period of 10-years? A hydrological engineer wants to design a small dam for a flood whose return period is 50 years. What risk are they willing to accept for the flooding to occur in the next 2 years?