Answer:
The probablility that there are 8 occurrences in ten minutes is 0.00518 or 0.5%.
Step-by-step explanation:
The distribution that represents the ocurrence of this events is the Poisson distribution.
The probability of having k events in a ten-minute-period can be expressed as:
[tex]P(x=k)=\frac{ \lambda^ke^{-k}}{k!}[/tex]
being λ the mean number of occurrences in ten minutes.
The probablility that there are 8 occurrences in ten minutes can be calculated as:
[tex]P(x=k)=\frac{ \lambda^ke^{-k}}{k!}\\\\P(x=8)=\frac{5.3^8e^{-8}}{8!}=\frac{(622596*0.000335463)}{40320}=0.00518[/tex]
The probablility that there are 8 occurrences in ten minutes is 0.00518 or 0.5%.
