Question

3. The long-term average October precipitation in Syracuse is 3.36 inches, with a standard deviation of 1.48 inches. Assuming a normal distribution, what is the probability that less than 1.0 inches of precipitation will occur in any October? What is the probability that more than 5.0 inches will occur? 4. (15 Points) A chemical industry discharges a waste contaminated with trichloroethylene (TCE) to the city sewer system. By law, the concentration of TCE must be 0.1 ug/L or less. To enforce this law, the Department of Environmental Conservation (DEC) conducts random testing. The chief environmental engineer for the chemical company knows that the mean TCE concentration in the waste is 0.064 ug/L, and the standard deviation is 0.022 ug/L. The TCE concentration can be assumed to be a normal random variable. a. What is the probability that the company will fail a random test by the DEC? [In other words, the probability that a random sample will have TCE > 0.1 ug/L.] b. What is the probability that the company will fail two consecutive random tests? The tests can be assumed to be independent of each other. c. Determine the concentration of TCE that is exceeded only 10% of the time.

Answer 1

3. Here distribution is normal with mean=3.36 and standard deviation=1.48

We need to find

P(Z <1)

As distribution is normal we can convert x to z

P(< 1) = P(Z < 1-3.36 0.3%) = P(Z < -1.59) = P(x > 1.59) = 0.0559 1.48

P(x > 5) = P(2> 5 - 3.36 -) = P(Z > 1.11) = 0.1335 1.48