Correct : 0.17 to 0.19

Traffic flow rate q = 360 vehicles per hour.

Converting to vehicles per second:

q = 360 / 3600 = 0.1 vehicles/second

When the number of vehicles follows a Poisson distribution, the time headway between successive vehicles follows an Exponential distribution.

The probability density function of headway t is:

f(t) = q × e^−qt

The probability that headway lies between t₁ and t₂ is:

P(t₁ ≤ t ≤ t₂) = e^−qt₁ − e^−qt₂

Here t₁ = 6 seconds and t₂ = 10 seconds.

Substituting values:

P(6 ≤ t ≤ 10) = e^{−0.1 × 6} − e^{−0.1 × 10}

P(6 ≤ t ≤ 10) = e^−0.6 − e^−1.0

P(6 ≤ t ≤ 10) = 0.5488 − 0.3679

P(6 ≤ t ≤ 10) = 0.1809

Rounding off to 2 decimal places:

P(6 ≤ t ≤ 10) = 0.18

Therefore the probability that the headway between successive vehicles lies between 6 and 10 seconds is 0.18 or 18%.