(3 points) The age of all farmers are normally distributed with a mean 51 years old and standard deviaiton 9 years old. Part A About middle 30% of farmers between 47_490 years old and 54.510 years old. (Rounding the answer to 3 decimal places if possible) Part B About middle 20% of farmers between 48.750 years old and 53.350 years old. (Rounding the answer to 3 decimal places if possible) (4 points) In a large company, the commute time of all employees are normally distributed with a mean of 50 minutes and a standard deviation of 3 minutes. Part A If 2 employees are selected at random, calculate the probability that the mean commute time of the selected employees is higher than 54.2 minutes by following the steps below. Step 1 - Summarizing the information about the Population Distribution of the commute time The population distribution is ? v with the mean of and the standard deviation of Step 2 - Determining the Sampling Distribution of the sample mean The sampling distribution is '? v with the mean of and the standard deviation of Note: Round the standard deviation (SD) to the 8 decimal places. Step 3 - Calculate the probability using the sampling distribution in Step 2 Probability = Note: Express the probability in decimal from and round it to 4 decimal places (e.g. 0.1234). Part B Interpret the probability in Part A by completing the follow. Suppose we take ? v random samples of ? v employees from the population. We expect about % of the selected samples produce a ? v ? v than (6 points) In Vancouver, the selling price of all one-bedroom condos are normally distributed with a mean of 659 thousand dollars and a standard deviation of 109 thousand dollars. Part A If 14 one-bedroom condos are selected at random, calculate the probability that the mean selling price of the selected one-bedroom condos is higher than 722.2 thousand dollars. Probability = Note: (1) Keep the standard deviation of the sampling distribution to at least 8 decimal places. (2) Express the probability in decimal form and round it to 4 decimal places (e.g. 0.1234). Part B If 31 one-bedroom condos are selected at random, calculate the probability that the mean selling price of the selected one-bedroom condos is lower than 615.1 thousand dollars. Probability = Express the probability in decimal form and round it to 4 decimal places (e.g. 0.1234). Part C If the distribuiton of selling price for all one-bedroom condos is NOT normal, will the probability in Part(A) still accurate? The probability is ? v . It is because (Select all that apply) A. the population distribution is not normal. B. the sample size is less than 30. c. the sample size is at least 30. D. the sampling distribution of the mean selling price may not be normal. E. the sampling distribution of the mean selling price is still normal. Part D If the distribuiton of selling price for all one-bedroom condos is NOT normal, will the probability in Part(B) still accurate? The probability is ? v . It is because (Select all that apply) A. the population distribution is not normal. B. the sample size is less than 30. c. the sample size is at least 30. D. the sampling distribution of the mean selling price may not be normal. E. the sampling distribution of the mean selling price is still normal