Question

Airline Fatalities One study showed that in a certain year, airline fatalities occur at the rate of 0.011 deaths per 100 million miles. Find the probability that, during the next 100 million miles of flight, there will be

Answer 1

`P(X = 0) = 0.9891`

Explanation:

Given

`\lambda = 0.011`

Required [This completes the question]

The probability of exactly 0 deaths

This probability follows a Poisson distribution, and it is given by:

`P(X = x) = (e^(-\lambda)\lambda^(x))/(x!)`

For 0 deaths;

`x = 0`

So, the expression becomes

`P(X = 0) = (e^(-\lambda)\lambda^(0))/(0!)`

`P(X = 0) = (e^(-\lambda)\lambda^(0))/(1)`

`P(X = 0) = (e^(-\lambda)*1)/(1)`

`P(X = 0) = e^(-\lambda)`

Substitute 0.011 for
`\lambda`

`P(X = 0) = e^(-0.011)`

`P(X = 0) = 0.9891`

The probability of having exactly death is 0.9891