Question: 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. (Chance, Summer 2005) The probability that an intruding object (e.g., a missile) will be detected on a flight track by SBIRS is 0.8. Consider a sample of 5 simulated tracks, each with an intruding object. Let x equal the number of these tracks on which SBIRS detects the object.

(a) Construct the entire binomial distribution.

(b) Find P(x = 3), the probability that SBIRS will detect the object on exactly 3 tracks.

(c) Find P(x > 2), the probability that SBIRS will detect the object on at least 2 tracks.

(d) Find P(x < 3), the probability that SBIRS will detect the object on 3 or less tracks.

(e) Graph the distribution using a histogram. Be certain to label your axes.