The merging process from an acceleration lane to the through lane of a freeway constitutes an important aspect of traffic operation at interchanges. A study of parallel interchange ramps in Israel revealed that many drivers do not use the entire length of parallel lanes for acceleration, but seek as soon as possible an appropriate gap in the major stream of traffic for merging (Transportation Engineering, Nov. 1985). At one site (Yavneh), 54% of the drivers use less than half the lane length available before merging. Suppose we plan to monitor the merging patterns of a random sample of 330 drivers at the Yavneh site.

a. What is the approximate probability that fewer than 100 of the drivers will use less than half the acceleration lane length before merging?

b. What is the approximate probability that 200 or more of the drivers will use less than half the acceleration lane length before merging?