Mobile homes are tightly constructed for energy conservation. This can lead to a

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 NO2 concentration in these structures.

(a) In one sample of mobile homes in the Los Angeles area, the mean NO2 concentration in kitchens during the summer was 37.26 ppb, and the standard deviation was 11.14. Making no assumptions about the shape of the NO2 distribution, what can be said about the percentage of observations between 14.98 and 59.54? (Round the answer to the nearest whole number.)
At least  %

(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 NO2 concentration during the winter was 24.74 ppb, and the standard deviation was 16.40. Do these values suggest that the histogram of sample observations did not closely resemble a normal curve? (Hint: What is x - 2s?)

Mobile hames are tightly canstructed for energy conservation. This can lead to a buildup of indoor pollutants. The paper 'A Survey of Nitragen Dioxide Levels Inside Mabile Homes" discussed various apccts of NO2 concentration in these structures. (a) In one sample of mobile homes in the Los Angeles area, the mean NO conentration in kitchens during the summer was 37.26 ppb, and the standard deviation was 11,14, Making no assumptions about the shape cf the NO distribution, what can be said about the penantaga of onservations bataen 14.08 and 59.54? (Round the nswer to the nearest whola numbar.) At least bInside what interval is it guarenteed that at least 99% ufthe coiceritration bservations will le? (c) In a sample o non-Los Angeles mabile homes, the average kitchen NO2 C normal curve? n during the winter was 24.74 ppb, and the standard deMation was 16.40. Do these values suggest tat the histogram ot sample observations did not closely resemble a Hint: what is x 25?) O Yes

Explanation / Answer

a)

here P(14.98 <X<59.54)=P((14.98-37.26)/11.14<K<(59.54-37.26)/11.4)=P(-2<K<2)

from Chenychev's inequality P(14.98 <X<59.54) >=(1-1/k2)*100 =(1-1/22)*100 =75.0%

At least 75.0%

b)

from Chebychev's at least 89% of the concentration observations will lie witin 3 std deviation from mean

hence interval =37.26-/+3*11.14 = {3.84 , 70.68]

c)

Yes (as x-2s will become negative and NO2 conc can not be negative)

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