During the painting of cars at a car factory, an error can occur which later leads to bubbles forming in the paint. One examines the paintwork of 32 cars and 8 of these have faults. The factory manager wants a 99% confidence interval for the proportion of cars with the fault.

a)

Estimate the error rate.

Round your answer to 3 decimal places.

b)

The interval should have a margin of error of 5%. How many cars must be examined for this to be achieved? The number must be valid regardless of how large or small the error rate is.

Round your answer to the nearest integer.

c)

The interval should have a margin of error of 5%. How many cars must be examined for this to be achieved? Assume that the error rate you estimated is the correct value.