Answer:
There is a 55.95% probability that, in the next 3,000 stars monitored by the Kepler mission, more than 4 planet transits will be seen.
Step-by-step explanation:
Assume that the number of planet transits discovered for every 3,000 stars follows a Poisson distribution with λ=5.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
is the Euler number
is the mean in the given time interval.
For this problem, we have that
What is the probability that, in the next 3,000 stars monitored by the Kepler mission, more than 4 planet transits will be seen?
That is . We either see 4 or less planets, or we see more than 4. The sum of the probabilities is decimal 1. So
In which
So
Finally
There is a 55.95% probability that, in the next 3,000 stars monitored by the Kepler mission, more than 4 planet transits will be seen.