The Space-Based Infrared System (SBIRS) uses satellite imagery to detect and track missiles (Chance, Summer 2005). 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.

b. Give the values of p and n for the binomial distribution.

c. Find P(x = 15), the probability that SBIRS will detect the object on exactly 15 tracks.

d. Find P(x ≥ 15), the probability that SBIRS will detect the object on at least 15 tracks.

e. Find E(x) and interpret the result.