The U.S. government has devoted considerable funding to missile defense research over the past 20 years. The latest development is the Space-Based Infrared System (SBIRS), which uses satellite imagery to detect and track missiles. The probability that an intruding object (e.g., a missile) will be detected on a flight track by SBIRS is .8. Consider a sample of 20 simulated tracks, each with an intruding object. Let x equal the number of these tracks where SBIRS detects the object.

a. Demonstrate that x is (approximately) a binomial random variable.

1. Give the values of p and n for the binomial distribution.
2. Find P(x = 15), the probability that SBIRS will detect the object on exactly 15 tracks.
3. Find P(x 15), the probability that SBIRS will detect the object on at least 15 tracks.
4. Find E (x) and interpret the result.