SOLUTION: 4.4.2 Suppose that over a period of several years the average number of deaths from a certain noncontagious disease has been 10. If the number of deaths from this disease follows t

Algebra ->  Probability-and-statistics -> SOLUTION: 4.4.2 Suppose that over a period of several years the average number of deaths from a certain noncontagious disease has been 10. If the number of deaths from this disease follows t      Log On


   

Question 1199410: 4.4.2 Suppose that over a period of several years the average number of deaths from a certain noncontagious disease has been 10. If the number of deaths from this disease follows the Poisson distribution, what is the probability that during the current year: a. Exactly seven people will die from the disease? b. Ten or more people will die from the disease?
Found 2 solutions by ElectricPavlov, ikleyn:
Answer by ElectricPavlov(122) About Me  (Show Source):
You can put this solution on YOUR website!
**a) Probability of Exactly Seven Deaths**
* **Poisson Distribution Formula:**
P(X = k) = (λ^k * e^(-λ)) / k!
where:
* X is the number of occurrences (deaths)
* λ is the average number of occurrences (10)
* k is the specific number of occurrences (7)
* e is the base of the natural logarithm (approximately 2.71828)
* **Calculate:**
P(X = 7) = (10^7 * e^(-10)) / 7!
P(X = 7) ≈ 0.0901
* **Probability of exactly seven deaths: 0.0901 or 9.01%**
**b) Probability of Ten or More Deaths**
* **Calculate the probability of fewer than ten deaths:**
P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)
* Calculate each probability using the Poisson formula as in part (a).
* **Probability of ten or more deaths:**
P(X ≥ 10) = 1 - P(X < 10)
* **Using a Poisson probability table or calculator:**
P(X ≥ 10) ≈ 0.5830
* **Probability of ten or more deaths: 0.5830 or 58.30%**
**Note:**
* You can use statistical software (like R, Python, or Excel) or online calculators to calculate Poisson probabilities more efficiently.
* The Poisson distribution assumes that events are independent and occur at a constant average rate.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
4.4.2 Suppose that over a period of several years the average number of deaths from a certain noncontagious disease has been 10.
If the number of deaths from this disease follows the Poisson distribution, what is the probability that during the current year:
a. Exactly seven people will die from the disease?
b. Ten or more people will die from the disease?
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As I read this problem, I see that it is defective.

To be correct, in the first sentence the problem must say that '10' is the average number of deaths per year.