Auto emissions oxides of nitrogen (called nox for short) emitted by cars and trucks are important contributors to air pollution. the amount of nox emitted by a particular model varies from vehicle to vehicle. for one light-truck model, nox emissions vary with mean μ = 1.8 grams per mile and standard deviation σ = 0.4 gram per mile. you test an srs of 50 of these trucks. the sample mean nox level will vary if you take repeated samples.

And for the standard deviation we have:

And then the distribution for the sample mean is:

Step-by-step explanation:

Assuming this question "Describe the shape, center, and spread of the sampling distribution of "

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

From the central limit theorem we know that the distribution for the sample mean is given by:

For this case we satisfy the condition that the sample size is large because n>30 so then we have:

And for the standard deviation we have:

And then the distribution for the sample mean is:

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step-by-step explanation:

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry