Stat 20 Review
Faculty: Professor Hank Ibser
Reviewer: Larry Wang,
Location: 101 Moffitt, Tu 5-7 PM
Study group: MW 1-2 201A Chavez , http://www.csrjjsmp.com/stat20.html /
Community through Academics and Leadership

Midterm 1 Review

  1. The average salary in a company is $30,000 with an SD of $50,000. Someone calculates the percent of people who have salaries above $50,000 using the normal curve. Is that calculation too large, too small, or about right?
  2. The average age of one group of 20 people is 25 years old with an SD of 5 years. The average age of a second group of 30 people is 15 years old also with an SD of 5.
  3. Find the average of the combined list
  4. Find the SD of the combined list
  5. Assume the ages are normally distributed. Someone claims to be younger than 70% from the first group and older than 60% of people from the second group. Is this claim reasonable? Explain.
  6. Say as much as you can about a list of numbers given: (each part refers to a different list)
  7. The SD of the list is 0
  8. The rms of the list is 0
  9. The mean of the list is 5 and the SD is 1. There are two numbers in the list.
  10. A shoelace factory produces shoelaces whose lengths follow the normal curve closely. The average length is 12 inches and the SD is 1 inch.
  11. True or false and explain: The standard normal curve is an appropriate histogram for this data.
  12. What is the percentage of shoelaces from this factory longer than 11 inches?
  13. What is the percentage of shoelaces from this factory shorter than 12.5 inches?
  14. What is the percentage of shoelaces from this factory between 10 and 13 inches?
  15. In a different shoelace factory, the answers to parts b and c are 97.7% and 84.2%, respectively. Assuming the products of this factory also follow the normal curve, what is the average and SD of their lengths?
  16. In a third shoelace factory, the answers to parts b and d are 69.1% and 86.6%, respectively. Assuming the products of this factory also follow the normal curve, what is the average and SD of their lengths?
  17. In a relay race, teams of 4 people are able to break up the 10-mile course however they like. On your team, the average speed each person can run is 0.15 miles per minute with an SD of 0.10 miles per minute. The average amount of time each person took to run their part was 20 minutes with an SD of 15 minutes. Note that each person ran a different distance. What is the correlation between the speed of a person and how much time they ran in the race?
  18. Tailors often use a series of approximations when making clothing so that they can use fewer measurements. A tailor measures a customer’s arm length, and wants to use it to predict torso length. Assume male arm length is normally distributed with a mean of 22 inches and an SD of 3 inches, and male torso length is the same. The correlation between the two is measured to be 0.6. Assume both of a person’s arms are the same length.
  19. The tailor’s apprentice measures a customer’s arm as 24 inches. How long will he predict the customer’s torso is?
  20. The tailor wants to be 95% certain that the actual torso length is within the predicted range. What value should his assistant report?
  21. Of men in the 90th percentile of arm length, how many are above the 90th percentile for torso length?
  22. Of those who have a 19-inch torso, what percent have an arm longer than 19 inches?
  23. Of those who have a 25-inch arm, what percent are above the 80th percentile for torso length?
  24. There is also a correlation of 0.6 between a person’s wrist diameter and arm length. Of those in the 30th percentile for arm length, what percent are above the 40th percentile for wrist diameter?
  25. An especially lazy apprentice measures a customer’s wrist diameter, hoping to use it to predict torso length. What correlation should he use?
  26. The average on the midterm was a 40 with an SD of 10 and the average on the final was 80 with an SD of 20. The correlation between the two is 0.6. The midterm was scored out of 100 points while the final was scored out of 150 points.
  27. Investigator R predicts the final score by using regression based on the midterm score. What is the RMS error for her method?
  28. Investigator A predicts the final score by guessing 80 all the time. What is the RMS error for his method?
  29. Investigator D predicts the final score by doubling the midterm score. Which RMS error is larger, Investigator R’s or Investigator D’s?
  30. *Calculate the RMS error for investigator D’s method.
  31. What is the correlation between Investigator A’s prediction and the actual midterm score?
  32. What is the correlation between Investigator D’s prediction and the actual final score?
  33. What is the correlation between Investigator R’s prediction and the actual midterm score?
  34. What is the correlation between Investigator R’s prediction and the actual final score?
  35. Calculate the RMS error for predicting final score as 100.
  36. *Calculate the RMS error for using the SD line to predict final score
  37. The weight and tail-length of rats have a correlation of 0.4. The scatter plot of the data is football shaped. The average weight is 50g with an SD of 10g. A rat at the 81st percentile of tail lengths has a tail that is 13 inches long while a rat at the 24th percentile has a tail that is 8 inches long. A scientist calculates the regression line for predicting tail lengths from weight as . Is this the correct regression line?
  38. (Ch 6 special review 10) A study was done that measured whether the subjects were right-handed or left-handed, as well as their ages. The study showed that the proportion of left-handed people and the ages had a strong negative correlation.
  39. True or false and explain: We can conclude that getting older causes people to become right-handed.
  40. True or false and explain: We can conclude that many people become right-handed as they grow older, but we cannot tell why.
  41. True or false and explain: We can conclude that older people tend to be more right-handed, but we cannot tell why.