Question

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" discussed various aspects of NO, concentration in these structures. (a) In one sample of mobile homes in the Los Angeles area, the mean No, concentration in kitchens during the summer was 37.28 ppb, and the standard deviation was 11.44. Making no assumptions about the shape of the NO, distribution, what can be said about the percentage of observations between 14.40 and 60.16? (Round the answer to the nearest whole number.) At least 0% (b) Inside what interval is it guaranteed that at least 89% of the concentration observations will lie? ( ? ? (c) In a sample of non-Los Angeles mobile homes, the average kitchen NO, concentration during the winter was 23.46 ppb, and the standard deviation was 17.40. Do these values suggest that the histogram of sample observations did not closely resemble a normal curve? (Hint: What is x - 2s?) Yes Ο Νο

Answer 1

Solution: (a): Since; of the underlying → we make no assumptions and Goo 16 as are → distribution The interval between 14.40 two Standard deviations → we must use Tcheby sheft's The ošem. P (1y-ukko) > = 1 - 2 - 4 P (14.40 <Y <60.16) - P (1y-31 28 2 2.2.88) • P(IY- 37291 22 ) >=1 31-1 : 1-0.25 = 0.756. At least 764

(b): Tchebysheff's Say's [1-4027-89.6. of the data lie with in 3 sold of the mean Lower limit : 37.28 -(3x 11.44) = 37.28 - 34:32 upper limit = 2.96 ; 37.28 + (3x 11.44) 37.28 + (34•32) = 71.6 :: At least 89% of the concentration observations cell lie between 12.96 and 71161 (C): yes! · It means the Samples do not resemble a normal Curve, because 25 is goat er than the mean, and it's impossible to have a negative number for a data point: -