Tracking missiles with satellite imagery. 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 .8. Consider a sample of 20 simulated tracks, each with an intruding object. Let x equal the number of these tracks on which 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.
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