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
i) what is the distribution of the sample proportion of cars turning right at this intersection, in random samples of this size?
ii) what is the probability that, in such a sample, the proportion turning right is between 0.28 and 0.32?
is a) binomial (n=15, p=3/10)
P(X>3)=.2969 or is there more to it then this?
b) i) Binomial (n=1428, p=3/10)
is there more to this?
and what would you answer for b) ii) b?