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Practice Final SU 2009

Answer use the following information for a producer

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Answer___________________ Use the following information for problems 33 – 35: A producer of infant formula wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities: 7
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r = 0.9 x = 6.5 y = 6.6 s x = 3.6 s y =1.2 33)Find the equation of the regression line. Answer___________________ 34)Using your equation predict the weight of an infant who is 6 months old. Answer___________________ 35) a) Find and interpret the value of r 2 for this problem. Answer___________________ b) At which point (x, y) on the regression line will you make the very best predictions? Answer___________________ 8
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Use the followi ng information for problems 36 and 37: A political science major has a job in which she stands outside the library trying to get students to register to vote. She knows that 3% of the students asked will result in a registration. 36) She asks three students at random. a) What is the chance that exactly one of them will register to vote? Answer___________________ b) What’s the chance that at least one of them will register to vote? Answer___________________ 37) She asks 400 students at random. What is the chance that more than 5% of them will register to vote? Answer___________________ 38) Results show that 80% of business majors graduate. You choose 5 business majors at random. What is the chance that at least 2 of them graduate? Answer___________________ Use the following information for problems 39 and 40: 9
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Casino A gets 60% of the business at a hotel and Casino B gets 40% of the business. 10% of Casino A players won money on their last visit. 12% of Casino B players won money on their last visit. Assume each casino player played at only one casino. 39)What percentage of all casino players at this hotel made money on their last visit? Answer___________________ 40)Suppose a casino player at this hotel won money on their last visit. Were they more likely to have played at Casino A or Casino B? Circle one: Casino A Casino B Justify your answer with probabilities : Use the following information for problems 41 and 42: A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean μ x = 298 ml and standard deviation σ x = 3 ml. 41) What is the probability that an individual bottle contains less than 294 ml? Answer___________________ 10
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42) What is the probability that the mean contents of the bottles in a six-pack is either less than 294 ml OR more than 302 ml? Answer___________________ Use the following information for problems 43 and 44: Gain communications sells equipment to both military and civilian populations. The mean and variance of the number of military sales per year (X) are µ x = 5,000 sales and σ 2 x = 500 sales 2 . The mean and variance of the number of civilian sales (Y) per year are µ y = 1,000 sales and σ 2 y = 100 sales 2 . 43)If civilian and military sales are dependent with a correlation of 0.6, a) What is the mean of the total number of sales per year for Gain Communications? Answer___________________ b) What is the standard deviation of the total number of sales per year for Gain Communications? Answer___________________ 44. Now suppose that military and civilian sales are independent. The profit from each military sale (X) is $2,000 and the profit from each civilian sale (Y) is $3,500. What is the mean of the total profit per year? Answer___________________ 11
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