Biology and Environmental Science Many lakes are carefully monitored for pH concentration, total phosphorus, chlorophyll, nitrogen, and total suspended solids. These data are used to characterize the condition of the lake and to chart year-to-year variability. Based on information from the Lake Partner Program, Ontario Ministry of the Environment, Aberdeen Lake has a mean total phosphorus concentration of 14.6 mg/liter and standard deviation 5.8 mg/liter. Suppose a day is selected at random, and a total phosphorus measure from Aberdeen Lake is obtained.
a. What is the probability that the total phosphorus is less than 13 mg/liter?
b. What is the probability that the total phosphorus differs from the mean by more than 5 mg/liter?
c. Suppose the total phosphorus is less than 20 mg/liter. What is the probability that it is less than 14 mg/liter?
d. If the total phosphorus measurement is 27 mg/liter, is there any evidence to suggest the mean has increased?