According to Statistics Canada, the proportion of residents in Nova Scotia, aged 18 and older who are obese is 35.3%. A group of healthcare researchers is conducting a survey of 166 Nova Scotians, and they want to make sure that their sampling was done well. One way they are planning on doing this is comparing the proportion of obese Nova Scotians in their sample to the census data. (a) Find the mean for the sample proportion for random samples of size 166. Mean = (Round your answer to three (3) decimal places). (b) Find the standard deviation for the sample proportion for random samples of size 166. Standard deviation = (Round your answer to three (3) decimal places). Suppose that 35.9% of the researchers' sample are obese. If the true percentage of Nova Scotians in the population that they sampled from that are obese was 35.3%, what is the probability that the researchers would observe a sample where more than 35.9% of the people were obese? (c) Calculate the z-score needed to help find this probability. Z-score = (Roound your answer to two (2) decimal places). (d) What is the probability that the researchers would observe a sample of size 166 where more than 35.9% of the people were obese? Probability = (Round your answer to three (3) decimal places). (d) What is the probability that the researchers would observe a sample of size 166 where less than 35.9% of the people were obese? Probability = (Round your answer to three (3) decimal places). (e) Suppose we take another random survey of size 61. How will the probability, that more than 35.9% of the sample will be obese, be affected? O A. It will be larger because the standard deviation will be larger. O B. It will be larger because the standard deviation will be smaller