An average of 15 aircraft accidents occur each year according to the world almanac and book of facts. if the number of aircraft accidents per year follows a poisson process, what is the probability of 36 or more accidents in a 2 year period?

15.87% probability of 36 or more accidents in a 2 year period

Step-by-step explanation:

I am going to approximate the normal probability distribution to the Poisson to solve this question.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Poisson probability distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval. The variance has the same value as the mean.

An average of 15 aircraft accidents occur each year

So for 2 years,

Approximation to the normal

What is the probability of 36 or more accidents in a 2 year period?

, which, using continuity correction, is , which is 1 subtracted by the pvalue of Z when X = 35.5.

has a pvalue of 0.8413

1 - 0.8413 = 0.1587

15.87% probability of 36 or more accidents in a 2 year period