The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model
ID: 3175973 • Letter: T
Question
The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.19 grams per mile (g/mi) and standard deviation 0.053 g/mi. Government regulations call for NOX emissions no higher than 0.26 g/mi.
What is the probability (±0.0001) that a single car of this model fails to meet the NOX requirement?
.0934
A company has 25 cars of this model in its fleet. What is the probability (±0.0001) that the average NOX level x¯ of these cars is above the 0.26 g/mi limit?
Explanation / Answer
mean is 0.19 and sd is 0.053
a) we need P(x>0.26)=P(z>(0.26-0.19)/0.053)=P(z>1.32) or 1-P(z<1.32). From normal distribution table it gives 1-0.9066 or .0934
b) we now need P(xbar>0.26)=P(z>(0.26-0.19)/(0.053/sqrt(25))=P(z>6.6) , from normal distribution table we get this probability close to 0
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