Question

Automobiles frequently arrive at the Bronte exit of the Queen Elizabeth Way at the rate of seven per minute. The distribution of arrivals approximates a Poisson distribution. a. What is the probability that no automobiles arrive in a particular minute? (Round the final answer to 4 decimal places.) Probability b. What is the probability that at least five automobile arrives during a particular minute? (Round the final answer to 4 decimal places.) Probability

statistics

Answer 1

a)

Here, λ = 7 and x = 0
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 0)
P(X = 0) = 7^0 * e^-7/0!
P(X = 0) = 0.0009
Ans: 0.0009

b)
Here, λ = 7 and x = 5
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X >=5) = 1 - P(X <= 4).
P(X > =5 ) = 1 - (7^0 * e^-7/0!) + (7^1 * e^-7/1!) + (7^2 * e^-7/2!) + (7^3 * e^-7/3!) + (7^4 * e^-7/4!)
P(X > =5) = 1 - (0.0009 + 0.0064 + 0.0223 + 0.0521 + 0.0912)
P(X > =5) = 1 - 0.1729 = 0.8271