A random sample of 16 mid-sized cars tested for fuel consumption gave a mean of 26.4 kilometers per litre with a standard deviation of 2.3 kilometers...

A random sample of 16 mid-sized cars tested for fuel consumption gave a mean of 26.4 kilometers

per litre with a standard deviation of 2.3 kilometers per litre.

A. Assuming that the kilometers per litre given by all mid-sized cars have a normal distribution,

find a 99% confidence interval for the population mean μ.

B. Suppose the confidence interval obtained in (a) is too wide. How can the width of this interval

be reduced? Describe all possible alternatives. Which alternative is the best and why?

The marks of 100 students in an examination are normally distributed with mean of 25 marks and astandard deviation of 10 marks.A. Given that the pass mark is 20, estimate the number of students who passed the examination.B. If 5.59% of the students obtain a distinction by scoring x marks or more, estimate the value ofx.C. If a sample of 20 students is selected, find the probability that the mean of the sample will beless than 27 marks