1. Lamb's-quarter is a common weed that interferes with the growth of corn. An agricultural researcher planted corn at the same rate in 16 small plots of land, then weeded the plots by hand to allow a fixed number of lamb's-quarter plants to grow in each meter of corn row. No other weeds are allowed to grow. Mean SD Weeds per meter 3.25 3.61 Yield 162.9125 8.66 If the correlation between the variables is -.457, answer the following questions. (a) What is the equation of the regression line? Write your answer in terms of the variables. (b) Interpret the slope in terms of the problem. (c) Does it make sense to interpret the y-intercept? If it does, interpret the intercept in terms of the problem. (d) What proportion of the variation in yield is explained by the equation of the regression line? 8. Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 30% of these tanks leak. You randomly choose 30 tanks at random. (a) Does the binomial setting apply? Explain. (b) What is the mean number of leaking tanks in such samples of 30 tanks? What is the standard deviation? (c) What is the probability that exactly 25 of these tanks leak? (d) What is the probability that at most 15 tanks leak in samples of 30 tanks? 9. The Wechler Adult Intelligence Scale (WAIS) is a common "IQ test" for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 100 and standard deviation 15. Use this information to answer the following questions. (a) What score places a randomly selected individual in the 95th percentile? (b) Describe the sampling distribution of the average WAIS score for an SRS of 60 people? (c) What is the probability that the average WAIS score of a SRS of 60 people is at least 105? 10. A SRS of 104 students were polled regarding a new sports team on campus. 37 of the 104 students said they would not be in support of the creation of the team. Calculate and interpret a 90% confidence interval for the true proportion of students who are not in favor of creating the team. 11. The scores on final exam grades for students taking the final at 8:00 am are given below. Check for outliers. 100 98 95 91.5 104.5 94 86 84.5 73 92.5 82 68.5 64.5 90.75 66.5 86.5 73.5 87 72.5 12. A forester measures the diameters of 40 redwood trees in a large wooded area that is for sale. It is known that the mean diameter of redwood trees is u = 10.4 feet and a standard deviation of o = 4.5 feet. (a) Describe the sampling distribution of the average diameter of the sample of 40 redwood trees. (b) What is the probability that the mean diameter of the sample of 40 redwood trees falls between 16 and 18 feet?