Normal Distribution Oxygen demand is a term biologists use to describe the oxygen needed by fi sh and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area in Marin County, California. In this wetland environment, the mean oxygen demand was m 5 9.9 mg L, with 95% of the data ranging from 6.5 mg L to 13.3 mg L (Reference: EPA Report 832-R-

93-005). Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal.

(a) Use the 95% data range to estimate the standard deviation for oxygen demand. Hint: See Problem 31 of Section 7.3.

(b) An oxygen demand below 8 mg/L indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg L?

(c) A high oxygen demand can also indicate trouble.

An oxygen demand above 12 mg/L may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg L?