Question

The Kepler telescope randomly searches for exoplanets (planets orbiting other stars in our galaxy). 20% of the exoplanets found by the Kepler telescope are in the “habitable zone,” a range of orbits around a star within which a planetary surface can support liquid water given sufficient atmospheric pressure. We are going to track the next 18 exoplanets that are discovered.

Use StatCrunch whenever possible. Copy and paste all StatCruch output used.

1. What is the probability that at least 10 of the discovered exoplanets are in the “habitable zone?” (6 points)

2. What is the probability that fewer than 7 of the discovered exoplanets are in the “habitable zone”? (6 points)

3. What is the probability that between 4 and 8 of the discovered exoplanets, inclusive, are in the “habitable zone?” (6 points)

4. What is the probability that less than 4 or more than 8 of the discovered exoplanets are in the “habitable zone?” (6 points)

5. If we track 18 exoplanets, how many “habitable zone” exoplanets would we expect to find on the average? (6 points)

Answer 1

Let X be a random variable representing the number of discovered exoplanets that are in the habitable zone. Then X is a Binomial Random variable with n=18 and p=0.2

the probability that at least 10 of the discovered exoplanets are in the “habitable zone

=

the probability that fewer than 7 of the discovered exoplanets are in the “habitable zone

=

the probability that between 4 and 8 of the discovered exoplanets, inclusive, are in the “habitable zone

=

the probability that less than 4 or more than 8 of the discovered exoplanets are in the “habitable zone

=

Expected number of exoplanets to find in the habitable zone is