The National Institute for Occupational Safety and Health (NIOSH) evaluated the level of exposure of workers to the chemical dioxin, 2,3,7,8-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 workers selected at the New Jersey plant, let represent the sample mean TCDD level.
a. Find the mean and standard deviation of the sampling distribution of Y̅.

b. Draw a sketch of the sampling distribution of Y̅. Locate the mean on the graph.

c. Find the probability that exceeds 550 ppt.

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.20 .10 500 1,000 1,500 2,000 TCDD level (ppt) Relative frequency