The level of nitrogen oxide (NOX) in the exhaust of a certain car model varies a
ID: 3155329 • Letter: T
Question
The level of nitrogen oxide (NOX) in the exhaust of a certain car model varies according to a normal distribution with a mean of 1.4 gal/mi, and a standard deviation of 0.3 gal/mi. In other words, if G is the NOX emission level for a car, then G ~ N(mu =1.4,sigma = 0.3) a. Let G be the variable for the mean NOX emission level for a sample of size n these cars of these cars 1. What is the distribution type for the statistic G ?Why? 2. Is this distribution exact or approximate? Why? 3. What is the mean of G ? 4. Suppose that a car rental company has a fleet of 125 such cars. What is the standard deviation of G for that fleet? b. What is the probability that, for a single car, the NOX emission will exceed 2.1 gal/mi? c. What is the probability that, for the fleet of 125 cars, the mean NOX emission will exceed 2.1 gal/mi?Explanation / Answer
1.
As the original distribution is normal, then G is also normal.
2.
It is exact, as the original distrbution is normal.
3.
By central limit theorem, it has the same mean, 1.4.
4.
By central limit theorem,
sigma(G) = sigma/sqrt(n) = 0.3/sqrt(125) = 0.026832816 [ANSWER]
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b.
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 2.1
u = mean = 1.4
s = standard deviation = 0.3
Thus,
z = (x - u) / s = 2.333333333
Thus, using a table/technology, the right tailed area of this is
P(z > 2.333333333 ) = 0.009815329 [ANSWER]
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c)
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 2.1
u = mean = 1.4
n = sample size = 125
s = standard deviation = 0.3
Thus,
z = (x - u) * sqrt(n) / s = 26.08745974
Thus, using a table/technology, the right tailed area of this is
P(z > 26.08745974 ) = 0 [ANSWER]
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