The owner of a petrol station wants to study fuel-purchasing habits of motorists at his station. A random sample of 60 motorists during a particular...

The owner of a petrol station wants to study fuel-purchasing habits of motorists at his station. A random sample of 60 motorists during a particular week gave the following results:

Amount purchased: = 42.8 litres, S =10.3 litres.

9 motorists purchased diesel.

(a) Set up a 95% confidence interval estimate for the proportion of motorists who buy diesel. Explain the meaning of your answer.                           

(b) Set up a 95% confidence interval estimate for the mean amount of fuel purchased by a customer. Explain the meaning of your answer.                    

(c) Before carrying out the survey, the owner thought that 10% of his customers used diesel, and that the average amount of fuel was no more than 40 litres per customer. Do the results of the survey suggest that he was wrong? Explain.

d)      Do we need to assume for the analysis in (b) that the amounts purchased follow a normal distribution? Discuss.