Question

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-8. The probability that there are 8 occurrences in ten minutes is

Answer 1

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:

$P(x=k)=\frac{ \lambda^ke^{-k}}{k!}$

being λ the mean number of occurrences in ten minutes.

The probablility that there are 8 occurrences in ten minutes can be calculated as:

$P(x=k)=\frac{ \lambda^ke^{-k}}{k!}\\\\P(x=8)=\frac{5.3^8e^{-8}}{8!}=\frac{(622596*0.000335463)}{40320}=0.00518$

The probablility that there are 8 occurrences in ten minutes is 0.00518 or 0.5%.