Chapter 4.4, Problem 41E

Mobile homes are tightly constructed for energy conservation. This can lead to a buildup of indoor pollutants. The paper “A Survey of Nitrogen Dioxide Levels Inside Mobile Homes” (Journal of the Air Pollution Control Association [1988]: 647–651) discussed various aspects of NO₂ concentration in these structures.

1. a. For one sample of mobile homes in the Los Angeles area, the mean NO₂ concentration in kitchens during the summer was 36.92 ppb, and the standard deviation was 11.34. Making no assumptions about the shape of the NO₂ distribution, what can be said about the percentage of observations between 14.24 and 59.60?
2. b. Inside what interval can you be sure that at least 89% of the concentration observations will lie?
3. c. For a sample of mobile homes that were not in Los Angeles, the average kitchen NO₂ concentration during the winter was 24.76 ppb, and the standard deviation was 17.20. Do these values suggest that the histogram of sample observations did not closely resemble a normal curve? (Hint: What is $\bar{x}-2s$?)