Mobile homes are tightly constructed for energy conservation. This can lead to a
ID: 3065215 • Letter: M
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 35.96 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 13.68 and 58.24? (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?
Explanation / Answer
SOlution:-
a) That interval is 2 std to the left and 2 std to the right of the mean. Chebyshev says there will be at least = 75% of the data in that interval.
k = 2
P(2 < k < 2) = (1 - 1/k2)
P(2 < k < 2) = 1 - 1/4
P(2 < k < 2) = 0.75
P(2 < k < 2) = 75%
b) The interval is it guaranteed that at least 89% of the concentration observations will lie is (2.54, 69.38).
According to Chebyshev says (1-(1/3)^2)% = 89% of the data lies within 3 std of the mean.
Lower limit: 35.96 - 3× 11.14 = 2.54
Upper limit: 35.96+3 ×11.14 = 69.38