Question 4 _ Apex company is one of the main producers of Nutrition bars in Australia. The Production manager of Apex company has reported that the weight of each Nutrition bar is a normally distributed random variable with a mean of 31.7g and a standard deviation of 0.3g. a. Find the probability that if a customer buys one chocolate bar, that bar will weigh less than 31.4g. ANSWER a): b. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be less than 31.4g. ANSWER b): c. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be greater than 31.4g. ANSWER c): d. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be between 31.4g and 31.9g. ANSWER d): b. Victorian government has proposed a new bus network to south east regional Victoria. A survey is sent out to residents asking questions which relate to: l. The resident's age 2. Frequency of bus use 3. Usual ticket type purchased 4. Main purpose of using the bus i. Describe the population ANSWER b {i}: ii. Indicate whether each of the questions above is categorical or numerical. ANSWER b {ii}: iii. Identify the possible scale of measurements on answers related to each of the questions. ANSWER b {iii}: iiii. Develop two more numerical questions and state whether the variables are discrete or continuous. ANSWER b {iv}: Question 5 a. Amiba Private limited produce 10 products in their production plant. The company's research and development (R& D) department wants to estimate a price for their 11th product. Hence, R & D department has selected 10 sites thought to have essentially identical sales potential and offered the product in each location at a different price. The resulting sales are recorded in the following table. You are required to nd the equation of the regression line and forecast the sales if company x the price at $15.25. (5 marks) ----m-tlmm m Sales 15 14 16 12 10 5 ($1100) ANSWER a): b. Victorian government has proposed a new bus network to south east regional Victoria. A survey is sent out to residents asking questions which relate to: 1. The resident's age 2. Frequency of bus use 3. Usual ticket type purchased 4. Main purpose of using the bus i. Describe the population ANSWER b {i}