SOLUTION: If 4% of the population carries a certain
genetic trait, hnd the probability that in a sample
of 100 people, there are exactly 8 people who have
the trait. Assume the distributi
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-> SOLUTION: If 4% of the population carries a certain
genetic trait, hnd the probability that in a sample
of 100 people, there are exactly 8 people who have
the trait. Assume the distributi
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Question 1199984: If 4% of the population carries a certain
genetic trait, hnd the probability that in a sample
of 100 people, there are exactly 8 people who have
the trait. Assume the distribution is approximately
Poisson. Answer by textot(100) (Show Source):
You can put this solution on YOUR website! **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%.**
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