Question: Workers exposed to dioxin. The Occupational Safety and Health Administration (OSHA) conducted a study to evaluate the level of exposure of workers to the dioxin TCDD. The distribution of TCDD levels in parts per trillion (ppt) of production workers at a Newark, New Jersey, chemical plant had a mean of 293 ppt and a standard deviation of 847 ppt (Chemosphere, Vol. 20, 1990). A graph of the distribution is shown here. In a random sample of n = 50 workers selected at the New Jersey plant, let y¯ represent the sample mean TCDD level.
(a) Find the mean and standard deviation of the sampling distribution of y¯.
(b) Draw a sketch of the sampling distribution of y¯. Locate the mean on the graph.
(c) Find the probability that y¯ exceeds 550 ppt.