Problem 5BSC

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(0), the probability that in a month, there will be no aircraft accidents. Is it unlikely to have a month with no aircraft accidents?

Answer:

Step 1:

The poisson distribution is applies,assume that the mean number of aircraft accidents in the United States is 8.5 per month.

The mean and variance of poisson distribution is same. That is ‘

Therefore

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 is a eulerian number.

e = 2.71828. ( constant value)

Here we have to find P(0), the probability that in a month, there will be no aircraft accidents.

Using the formula for Probability mass function of poisson distribution, we have

P(x = 0) = = 0.000203.

Yes, it is unlikely to have a month with no aircraft accident since the usual number of aircraft accidents.

Using the range rule of thumb,

Minimum = μ – 2σ

= 8.5 - 2()

= 2.66 accidents.

Maximum = μ + 2σ

=8.5 + 2()

= 14.33 accidents.