Question 1195988
**1. Probability Distribution of X**

* **If the number of arrivals per hour follows a Poisson distribution, then the time between arrivals follows an Exponential distribution.**

**2. Probability that Arrival Time is Greater Than 10 Minutes**

* **Convert minutes to hours:** 10 minutes = 10/60 hours = 1/6 hour 
* **Exponential Distribution:**
    * The probability density function (PDF) of an exponential distribution is: 
        * f(x) = λ * e^(-λx) 
        * where:
            * λ is the rate parameter (average number of arrivals per unit time) = 6 cars/hour
            * x is the time between arrivals (in hours)

* **Cumulative Distribution Function (CDF):**
    * The probability of the time between arrivals being less than or equal to 't' is given by:
        * F(t) = 1 - e^(-λt)

* **Probability of Arrival Time Greater Than 10 Minutes:**
    * P(X > 1/6) = 1 - P(X ≤ 1/6) 
    * P(X > 1/6) = 1 - F(1/6)
    * P(X > 1/6) = 1 - (1 - e^(-6 * (1/6)))
    * P(X > 1/6) = 1 - (1 - e^(-1))
    * P(X > 1/6) = e^(-1) 
    * P(X > 1/6) ≈ 0.3679

**Therefore, the probability that the arrival time is greater than 10 minutes is approximately 0.3679 or 36.79%.**