ENVR 890-2 Problem Set – April, 16, 2009

Note: This problem set is due on April 26, 2002. You are expected to work independently and not as groups in answering these questions and analyzing these data.

1. Below are data for the levels of a bacterial pathogen in a recreational water and drinking water supply.

Please analyze the data and answer the following questions about these data as directed or explained below.

Pathogen concentrations/L in untreated drinking water

Weekly Concentrations per Liter
Concentration/L, Jan-June / Concentration/L July-Dec
18.5 / 42.5
5 / 11
225 / 234
191 / 161
21 / 149
49 / 149
325 / 687.5
24 / 160
14 / 136
1807.5 / 100
60 / 81
52.5 / 1235
114 / 345
7.5 / 132.5
32.5 / 87.5
77.5 / 331
304 / 309
7.5 / 1662.5
10 / 175
42.5 / 21
4 / 27.5
2.5 / 29
10 / 35
30 / 39
5 / 15

For the data in the table above:

a. Determine the following for of the data (both columns):

Arithmetic mean

Geometric (log10) mean

Median

Standard deviation (arithmetic and log10)

95% confidence interval (arithmetic and log10)

Range (arithmetic and log10)

b. Plot (draw a graph) the frequency distribution of the data

c. Plot a cumulative frequency distribution of the data

d. Determine or estimate if the data are better described as: normally distributed or log-normally distributed.

e. The allowable geometric mean concentration of this pathogen in water for recreational use is 10 per liter and the maximum allowable is not to exceed (must be less than) 100 per 1 L 95% of the time. Do the concentrations meet these requirements based on:

1. arithmetic mean?

2. Geometric mean?

3. If neither, what percentage of the time does the water meet these two targets as determined from the frequency distribution?

f. The water is also used for drinking water supply and must be treated to reduce the pathogen concentration to an average of 0.1/L and a maximum of 1/L. What percentage and log10 reductions need to be achieved for the concentrations in the water to be reduced to these levels based on:

1. arithmetic mean concentration?

2. Geometric mean concentration

3. Maximum concentration?


2. Tabulated below are the dose-response data from a clinical study of gastrointestinal illness (GI) and microbial dose administered to sets of human volunteers.

A. Plot the data for the relationship between GI illness rates and microbial dose and draw a line through the points to define the dose-response curve.

B.  From your examination of these plotted data, does there appear to be an association?

C.  If there is an association, what kind is it or how would you describe it?

D.  If there is a dose-response relationship, determine the dose of organisms that corresponds to a GI illness risk of 50%.

E.  What are the risks of GI illness for the allowable concentrations for recreational water at 10 and at 100 per liter, assuming that a person ingested 0.1liter per exposure event?

F.  What are the risks of GI Illness for ingestion of a liter of water at the allowable concentrations in drinking water based on a mean of 0.1/L and a maximum of 1/l?

G.  If you set the maximum acceptable level of GI illness at 0.01%, what would be the corresponding dose of organisms associated with this risk?

Log10 No. Organisms/Dose % Gastrointestinal Illness

6 / 100
5 / 20
4 / 3
3 / 0.5
2 / 0.1
1.5 / 0.05


3. Tabulated below are the results of disinfection studies in which a suspension of the pathogens in water were dosed 3 different disinfectants. At various times after dosing, samples were taken to determine the number of viable microbes remaining (number of survivors), and these values were converted to a percentage of the initial number of organisms.

a. On the graph below or using software, plot the percentage of initial microbes remaining as a function of time.

b. Draw the lines for the "inactivation curves" of each microbe.

c. From the graph, estimate the times for 99.9% inactivation:

Disinfectant A:______Disinfectant B:______Disinfectant C: ______

e. What are the shapes of the disinfection curve and what are the nature of the disinfection kinetics?

Microbe A:______Microbe B:______Microbe C:______

Percent (%) Remaining

Contact Time (min) Microbe A Microbe B Microbe C

0 100 100 100

5 80 45 20

10 60 18 3

15 40 7.5 1

20 6 3.0 0.5

25 0.6 1.3 0.2

30 0.06 0.6 0.01

0 5 10 15 20 25 30

f. At what contact time will each disinfectant reduce the geometric mean pathogen concentration in the source water of question 1 to:

1. 1.1/L Disinfectant A______Disinfectant B______Disinfectant C______

2. 0.1/L Disinfectant A______Disinfectant B______Disinfectant C______