Question

4.. When you get an eye test in America, they often report your vision using a phrase like “20 20 vision” or “20 15 vision”. The phrase “A B vision” means that if you can (just barely) read the chart at A feet away, then the average person would need to stand B feet away to (just barely) read the chart.

a. Explain if “20 15 vision” is worse than average, average, or better than average vision.

b. It is possible to always set A = 20 (through rescaling) and then the only issue is figuring out B for a given person. Suppose that B is normally distributed with mean 20 feet and standard deviation 10 feet. Suppose you use the term “legally blind” if a person’s vision with corrective lenses is 20 40 or worse. Suppose you give someone an “unrestricted driver’s license” if their vision is 20 30 or better. What percentage of Americans won’t meet the definition of either label? Use R to help and include a picture in your answer.

c. Explain why it is somewhat strange to use a normal distribution to model B.

Answer 1