during any 2) Assume that the amount of carbon dioxide emitted by a car at a cer

Question

during any 2) Assume that the amount of carbon dioxide emitted by a car at a certain parking lot during any given 30-minute interval is uniformly distributed between 0 and 30 grams. If there are 230 cars at the parking lot in the next half-hour, and if we assume independence of the amounts emitted by cthe next half-hour andifrted betiveen 0 and 30 grans, by cars, a) what is the approximate probability that the total amount of the emitted carbon dioxide in the parking lot exceeds 3.3 kg? b) not more than what amount of carbon dioxide will be emitted with approximately 90% probability in the parking lot?

Explanation / Answer

for uniform distribution paramter a =0 and b=30

therefore mean =(0+30)/2 =15

and std deviation =(b-a)/(12)1/2 =8.6603

therefore expected amount of 230 observations =15*230=3450

and std error =std deviation*(n)1/2 =8.6603*(230)1/2 =131.339

a)

hence probability that weight exceeds 3.3Kg(3300 gm) =P(X>3300)=1-P(X<3300)=1-P(Z<(3300-3450)/131.339)

=1-P(Z<-1.1421)=0.8733

b) for 90th percentile ; z =1.2816

therefore corresponding value =mean +z*std deviation =3618.32 gm

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