Question

The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is

1. 0.029
2. 0.034
3. 0.039
4. 0.044

Answer 1

Correct Answer - Option 2 : 0.034

Concept:

Poisson distribution

According to the Poisson distribution probability of x = k is given by:

\(P\left( {x = k} \right) = \frac{{{\lambda ^k}{e^{ - \lambda }}}}{{k!}}\)

Calculation:

Given:

λ = 5.2

Let x be random variable which follows Poisson’s distribution

P(x < 2) = P(x = 0) + P(x = 1)

\(= \frac{{{{\rm{e}}^{ - {\rm{\lambda }}}}{{\rm{\lambda }}^0}}}{{0!}} + \frac{{{{\rm{e}}^{ - {\rm{\lambda }}}}}}{{1!}}{{\rm{\lambda }}^1} = {{\rm{e}}^{ - 5.2}}\left( {1+5.2} \right) = 0.0055 \times 6.2 = 0.034\)