You did not state the options to choose from, but I will give a suitable distribution for solving the given problem.
Answer:
Poisson Distribution
Explanation:
Poisson Distributions are used in calculating the probability of an event occurring over a given interval.
It is calculated using the formula
P(X = x) = [e^(-β)β^x]/x!
Where e = 2.718
β = mean or expected value of the variable.
x = number of successes of the event
Applying this to the given problem, suppose we are trying to find the probability that exactly four cars will arrive in 5 minute interval.
Average number of cars arriving = 3/10 = 0.3
The probability of success over a short interval must be the same probability over a long interval, so we have β = 0.3 × 5 = 1.5
x = 4
P(X = 4) = [e^(-1.5) (1.5)^(4)]/4!
= 0.047066518
≈ 0.0047
There is a 0.47% chance that exactly four cars will arrive in 5 minute interval.