1. Over the past 50 years, there has been a strong negative correlation between average annual income and the record time to run 1 mile. In other words, average annual incomes have been rising while the record time to run 1 mile has been decreasing.

1. Do you think increasing incomes cause decreasing times to run the mile? Explain.
2. What lurking variables might be causing the change in one or both of the variables? Explain.

2. Trevor conducted a study and found that the correlation between the price of a gallon of gasoline and gasoline consumption has a linear correlation coefficient of -0.7. What does this result say about the relationship between the price of gasoline and consumption? The study included gasoline prices ranging from $2.70 to $5.30 per gallon. Is it reliable to apply the results of this study to prices of gasoline higher than $5.30 per gallon? Explain.

3. What is the law of large numbers? If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.

4. According to a recent Harris Poll of adults with pets, the probability that the pet owner cooks especially for the pet either frequently or occasionally is 0.24.

1. From this information, can we conclude that the probability a male owner cooks for the pet is the same as for a female owner? Explain.
2. According to the poll, the probability a male owner cooks for his pet is 0.27, whereas the probability a female owner does so is 0.22. Lets explore how such probabilities might occur. Suppose the pool of pet owners surveyed consisted of 200 pet owners, 100 of whom are male and 100 of whom are female. Of the pet owners, a total of 49 cook for their pets. Of the 49 who cook for their pets, 27 are male and 22 are female. Use relative frequencies to determine the probability a pet owner cooks for a pet, the probability a male owner cooks for his pet, and the probability a female owner cooks for her pet.

5. You are applying for two jobs, and you estimate the probability of getting an offer for the first job is 0.70 while the probability of getting an offer for the second job is 0.80. Assume the job offers are independent.

1. Compute the probability of getting offers for both jobs. How does this probability compare to the probability of getting each individual job offer?
2. Compute the probability of getting an offer for either the first or the second job. How does this probability compare to the probability of getting each individual job offer? Does it seem worthwhile to apply for both jobs? Explain.

6. Consider a binomial distribution of 200 trials with an expected value of 80 and standard deviation of about 6.9. Use the criterion that it is unusual to have data values more than 2.5 standard deviations above the mean or 2.5 standard deviations below the mean to answer the following questions:

1. Would it be unusual to have more than 120 successes out of 200 trials? Explain.
2. Would it be unusual to have fewer than 40 successes out of 200 trials? Explain.
3. Would it be unusual to have from 70 to 90 successes out of 200 trials? Explain.

• Requirements: Complete the above questions. Be specific. For any numerical problem-solving questions, please provide the careful numerical procedure about how you reach the final answer, i.e. show your work.