A recent study investigated the relationship between car weight (lbs) and fuel efficiency (mpg) and obtained the following regression equation: = 75.340.046 2 =64.3% a) Which variable is the response variable? b) What is the correlation between weight and fuel efficiency? Show your work! c) Explain your correlation coefficient in context. Make sure to talk about both the strength and direction of the given variables in context. d) Is the y-intercept meaningful in this situation? Why or why not? Give a sound statistical justification. e) Explain the slope in context. f) A car has a weight of 804 lbs and a fuel efficiency of 24.9 mpg. Calculate the residual of this car. Show your work!

2. According to the American Veterinary Medical Association, the proportion of households owning a dog is 0.37. Assume the events are independent. a) If one household is randomly selected, what is the probability that the households does not own a dog? b) If four households are randomly selected, what is the probability that all four own a dog? c) If four households are randomly selected, what is the probability that at least one owns a dog? 3 Let's assume that the weights in kilograms (kg) of healthy adult female pigs from Abel Tasman National Park in New Zealand are normally distributed with mean 44 kg and standard deviation 3.1 kg. Include your normal curve for all parts and shade the area! a) What weight represents the middle 55% of pig weights? b) What is the probability that a single pig captured at random weighs within 3 kg of the mean weight? c) What is the probability that a single pig captured at random weighs more than 50 kg? d) What weight represents the top 34% of pig weights?