Question

On the average, two students per hour report for treatment to the first-aid room of a large elementary

school. What is the probability that, during a given hour…

1.Three students come to the first-aid room for treatment?

2.Two or fewer students will report to the first-aid room?

3.Between three and five students, inclusive, will report to the first-aid room?

4.More than two students will come to the first-aid room?

Answer 1

#1.
Here, λ = 2 and x = 3
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 3)
P(X = 3) = 2^3 * e^-2/3!
P(X = 3) = 0.1804
Ans: 0.1804

#2.
We need to calculate P(X <= 2).
P(X <= 2) = (2^0 * e^-2/0!) + (2^1 * e^-2/1!) + (2^2 * e^-2/2!)
P(X <= 2) = 0.1353 + 0.2707 + 0.2707
P(X <= 2) = 0.6767

#3.
We need to calculate P(3 <= X <= 5)
P(3 <= X <= 5) = (2^3 * e^-2/3!) + (2^4 * e^-2/4!) + (2^5 * e^-2/5!)
P(3 <= X <= 5) = 0.1804 + 0.0902 + 0.0361
P(3 <= X <= 5) = 0.3067

#4.
P(X > 2) = 1 - 0.6767 = 0.3233