A"planet transit" is a rare celestial event in which a planet appears to cross in front of its star as seen from earth. the planet transit causes a noticeable dip in the star's brightness, allowing scientists to detect a new planet even though it is not directly visible. the national aeronautics and space administration (nasa) recently launched its kepler mission, designed to discover new planets in the milky way by detecting extrasolar planet transits. after one year of the mission in which 3,000 stars were monitored, nasa announced that 5 planet transits were detected. (nasa, american astronomical society, jan. 4, 2010.) assume that the number of planet transits discovered for every 3,000 stars follows a poisson distribution with λ=5. what is the probability that, in the next 3,000 stars monitored by the kepler mission, more than 4 planet transits will be seen?

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.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have