Respuesta :
Answer:
a) 0.01111
b) 0.4679
c) 0.33747
Step-by-step explanation:
We are given the following in the question:
The number of accidents per week can be treated as a Poisson distribution.
Mean number of accidents per week = 4.5
[tex]\lambda= 4.5[/tex]
Formula:
[tex]P(X =k) = \displaystyle\frac{\lambda^k e^{-\lambda}}{k!}\\\\ \lambda \text{ is the mean of the distribution}[/tex]
a) No accidents occur in one week.
[tex]P(x =0)\\\\= \displaystyle\frac{4.5^0 e^{-4.5}}{0!}= 0.01111[/tex]
b) 5 or more accidents occur in a week.
[tex]P( x \geq 5) = 1-\displaystyle \sum P(x <5)\\\\=1=\displaystyle\sum_{x=0}^{x=4}\displaystyle\frac{4.5^x e^{-4.5}}{x!}\\\\ = 1-0.53210\\\\=0.4679[/tex]
c) One accident occurs today.
The mean number of accidents per day is given by
[tex]\lambda = \dfrac{4.5}{7} = 0.64[/tex]
[tex]P(x =1)\\\\= \displaystyle\frac{0.64^1 e^{-0.64}}{1!}= 0.33747[/tex]
