Answer:
The probability that at least two-third of vehicles in the sample turn is 0.4207.
Explanation:
Let X = number of vehicles that turn left or right.
The proportion of the vehicles that turn is, p = 2/3.
The nest n = 50 vehicles entering this intersection from the east, is observed.
Any vehicle taking a turn is independent of others.
The random variable X follows a Binomial distribution with parameters n = 50 and p = 2/3.
But the sample selected is too large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
Check the conditions as follows:

Thus, a Normal approximation to binomial can be applied.
So,

Compute the probability that at least two-third of vehicles in the sample turn as follows:



Thus, the probability that at least two-third of vehicles in the sample turn is 0.4207.