4.74 Rare planet transits. A planet transit\" is a rare celestial event in which

Question

4.74 Rare planet transits. 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 Na- tional Aeronautics and Space Administration (NASA) re- cently 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 plan- et 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 =5. What is the probability that, in the next 3,000 stars monitored by the Kepler mission, more than 10 planet transits will be seen?

Explanation / Answer

= 5

P(x) = (e^-)(^x) / x!

P(x > 10) = 1 - P(x 10) = 1 - P(0) - P(1) - P(2) ... - P(10)

= 1 - (e^-5)(5^0) / 0! - (e^-5)(5^1) / 1! - (e^-5)(5^2) / 2! - ... - (e^-5)(5^10) / 10!

= 1 - 0.0067 - 0.0337 - 0.0842 - ... - 0.0181

= 0.0137

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