Question: Suppose that only 60% of all drivers wear seat belts at all times. In a random sample of 500 drivers let X denote the number of drivers who wear seat belt at all times.
(a) State the exact distribution of X and use R to find P(270 ≤ X ≤ 320).
(b) Use the DeMoivre-Laplace Theorem, with and without continuity correction, to approximate P(270 ≤ X ≤ 320). Comment on the quality of the approximation provided by the two methods.