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Auto emissions Oxides of nitrogen (called NOX for short) emitted by cars and trucks are
Chapter 8, Problem 6(choose chapter or problem)
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 \(\mu=1.8\) grams per mile and standard deviation \(\sigma=0.4\) gram per mile. You test an SRS of 50 of these trucks. The sample mean NOX level \(\bar{x}\) will vary if you take repeated samples.
(a) Describe the shape, center, and spread of the sampling distribution of \(\bar{x}\)
(b) Sketch the sampling distribution of \(\bar{x}\) Mark its mean and the values 1, 2, and 3 standard deviations on either side of the mean.
(c) According to the 68-95-99.7 rule, about 95% of all values of \(\bar{x}\) lie within a distance m of the mean of the sampling distribution. What is m? Shade the region on the axis of your sketch that is within m of the mean.
(d) Whenever \(\bar{x}\) falls in the region you shaded, the unknown population mean \(\mu\) lies in the confidence interval \(\bar{x} \pm m\). For what percent of all possible samples does the interval capture \(\mu\)?
Questions & Answers
QUESTION:
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 \(\mu=1.8\) grams per mile and standard deviation \(\sigma=0.4\) gram per mile. You test an SRS of 50 of these trucks. The sample mean NOX level \(\bar{x}\) will vary if you take repeated samples.
(a) Describe the shape, center, and spread of the sampling distribution of \(\bar{x}\)
(b) Sketch the sampling distribution of \(\bar{x}\) Mark its mean and the values 1, 2, and 3 standard deviations on either side of the mean.
(c) According to the 68-95-99.7 rule, about 95% of all values of \(\bar{x}\) lie within a distance m of the mean of the sampling distribution. What is m? Shade the region on the axis of your sketch that is within m of the mean.
(d) Whenever \(\bar{x}\) falls in the region you shaded, the unknown population mean \(\mu\) lies in the confidence interval \(\bar{x} \pm m\). For what percent of all possible samples does the interval capture \(\mu\)?
Step 1 of 6
Given,
Sample size,
The NOX emissions mean,
The standard deviation,
