Assume i have a set of streamflow data that are recorded in Year 2016, and the following instructions are given,

1) Check whether or not the streamflow data follow a lognormal distribution (in other words, if the logarithms of the data

follow a Gaussian distribution). We will apply a Chi-square test for this purpose, with 5% significance.

What conclusions can you draw from this analysis?

2) Also, test the Gaussianity of the logarithms of the flows through a Gaussian probability

plot. What do you conclude from this analysis?

3) Through a routine water quality analysis, it is found that somebody has illegally dumped paint in

the river. This paint has been found downstream of an area with 50 houses. This means that any

of these 50 houses could have polluted the water. Through analyzing the houses, a consultant has

determined that there is an 90% chance that the paint used by household A is the paint that is found

in the water. Does this mean that there is an 90% chance that household A is guilty of polluting

the stream? If yes, explain your reasoning. If not, calculate the chance that the household is guilty,

and explain your reasoning.

4) The council decides to perform a water quality check every day. This test costs $500 each day. If a

pollutant is found in the water, they assume that they will find the pollutor, and they will fine them

$50,000. What does the probability to find a pollutant in the sample each day at least have to be,

for the council to be 90% sure that they will not lose money on these tests, in a non-leap year?

5) The council is contemplating organizing nature walks along the river with a paid guide. The walks

last for a day, and the guide charges $50 per customer per day. The salary of the guide is $1100

per week, and he is expected to guide at least 25 people per week. How certain can the council be

that they will be cash-flow positive any random week?