NOTE: Due to limitations in D2L, the following questions will each use their own set of data for the survey sample size and probability of support. Make sure you read each question carefully to make sure you answer each question correctly. Question 5 (4 points) Suppose that the survey is distributed to 105 individuals and an estimated 40% of the population supports the change. First calculate the expected number of Successes and Failures and enter the results into blanks 1 and 2 (since p is given as the proportion that support the change, assume that a success is if a respondent supports rezoning). Blank # 1 Blank #2 2 Question 6 (4 points) Suppose that the survey is distributed to 85 individuals and an estimated 35% of the population supports the change. Next, calculate the mean and standard deviation of the Normal Approximation and enter your answers into blanks 1 and 2. Round both answers to two decimal places. Blank #1 Blank # 2 A Question 7 (2 points) Suppose that the survey is distributed to 105 individuals and an estimated 35% of the population supports the change. Lastly, calculate the probability that 34 of the 105 respondents support the rezoning. Express your answer with four decimal places, and don't forget about the Continuity Correction Factor! 4 Suppose that a manufacturing facility is producing a support beam that is intended to be exactly 10 cm in length, however the beam can be as short as 9.75 cm or as long as 10.5 cm and still fulfill its purpose. Assume that the variation in beam lengths can be modeled as a Normal Distribution, and answer the following questions. Question 1 (2 points) Suppose that the average beam produced is slightly too short at 9.9 cm with a standard deviation of 0.4 cm. What is the probability that a bar chosen at random would be 9 cm or less? Round your answer to four decimal points. A Question 2 (2 points) Suppose instead that the average beam produced has a length of 9.5 cm with a standard deviation of 0.5. What is the probability that a bar chosen at random would be 9.3 cm or more? Express your answer with four decimal points. A Question 3 (2 points) Suppose that a new version of the product is released which has looser tolerances. Also suppose that management had enough foresight to re-center the manufacturing process to 10 cm and lowered the standard deviation to 0.3 cm. Further suppose that the new tolerances are between 9.5 and 10.5; use P(X