A sample of $400$ motorists from a country includes $40$ owners of a brand A car.

Construct a confidence interval, at the $0\mathrm{.}95$ confidence level, for the true proportion of motorists in this country who own a brand A car.

Answer the same question if the sample is of type $($equal probabilities without replacement$)$ and if the size of the population is:

$($a$)$ N$=5000$

$($b$)$ N$=1,000,000$