Aircraft Accidents. Assume that the Poisson distribution applies, assume that the mean number of aircraft accidents in the United States is8.5per month (based on data from the National Transportation and Safety Board), and proceed to find the indicated probability.

Find P(10), the probability that in a month, there will be 10 aircraft accidents. Is it unlikely to have a month with exactly 10 aircraft accidents?

Problem 7BSC

Answer:

Step1 of 1:

We have the mean number of aircraft accidents in the United States is 8.5 per month.

Consider a random variable “x” follows poisson distribution with sample size “n” and proportion “p”.

i,e.X P()

Probability mass function of poisson distribution is given by

P(x) = , x = 0,1,2,...,n.

Where, e = 2.71828.

We need to find P(10) = ?

Consider,

P(x) =

P(x = 10) =

=

= 0.1103.

Having 10 aircraft accidents in a month not unlikely because 10 falls within the usual range of values given in number(5).