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 m = 1.8 grams per mile and standard deviation s = 0.4 gram per mile. You test an SRS of 50 of these trucks. The sample mean NOX level x - will vary if you take repeated samples.
(a) Describe the shape, center, and spread of the sampling distribution of x¯.
(b) Sketch the sampling distribution of 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 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 x¯ falls in the region you shaded, the unknown population mean m lies in the confidence interval x - ± μ. For what percent of all possible samples does the interval capture μ?