Question 1199984
**1. Determine the Average Number of Occurrences (λ)**

* **λ = n * p** 
    * Where:
        * n = sample size (100 people)
        * p = probability of the trait (0.04) 
    * λ = 100 * 0.04 = 4

**2. Use the Poisson Probability Mass Function**

* The probability of observing exactly *k* events in a Poisson distribution is given by:

   * P(X = k) = (e^(-λ) * λ^k) / k! 

   * Where:
      * X is the random variable representing the number of people with the trait
      * λ is the average number of occurrences (4)
      * k is the desired number of occurrences (8)
      * e is the base of the natural logarithm (approximately 2.71828)
      * k! is the factorial of k (k! = k * (k-1) * (k-2) * ... * 1)

* **Calculate P(X = 8):**

   * P(X = 8) = (e^(-4) * 4^8) / 8! 
   * P(X = 8) ≈ (0.0183 * 65536) / 40320 
   * P(X = 8) ≈ 0.0298

**Therefore, the probability that in a sample of 100 people, exactly 8 people have the genetic trait is approximately 0.0298 or 2.98%.**