2 Question 2 (worth 9 marks)

(a) The local water supply is deemed to be contaminated with a heavy metal if the concentration of

this metal in the water is greater than 0.5 g L-¹. An environmental engineer has been contracted

to undertake six independent measurements (at different locations) of this water supply and has

obtained the following raw data:

Location

1

2

3

4

5

6

Concentration (g L-¹) 0.43 0.64 0.59 0.54 0.73 0.49

i) (2 marks) Calculate the sample average concentration (X) and sample standard deviation (s)

of this data.

ii) (3 marks) Using an appropriate statistical test, report on what evidence (if any) there is to

suggest that the local water supply is contaminated. State all assumptions used to obtain your

conclusion.

(b) (2 marks) When drilling for raw materials of copper and nickel, the amount of copper obtained

per cubic metre is typically C=460±140 kg (mean ± standard deviation) and the amount of

nickel obtained per cubic metre is typically N=180±30 kg (mean ± standard deviation). If the

amounts of copper and nickel obtained per cubic metre are positively correlated, with a correlation

of Corr(C, N)=0.4, calculate the mean and standard deviation of the total amount of raw materials

obtained per cubic metre (i.e. mean and standard deviation of C+ N).

(c) (2 marks) In a production line that makes resistors, 5 resistors are discarded per hour on average

due to defects. What is the probability of discarding at least 25 resistors in any 4-hour time period?