I can't work out how to do this question. It doesn't look like anything we've done before, but I don't know if I'm just misreading it. I'm assuming it has something to do with binomial distributions, but I'm not sure. Any help is appreciated!
A road is constructed so that the right-turn lane at an intersection has a capacity of 3 cars. Suppose that 30% of cars approaching the intersection want to turn right, and they do so independently.
a) If 15 cars approach the intersection, what is the probability that the right-turn lane will not hold all the cars wanting to turn right?
b) Over a week, 1428 cars used the intersection. What is the distribution of the sample proportion of cars turning right at this intersection, in random samples of this size?