Tracking missiles with satellite imagery. 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 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 P1x = 152, the probability that SBIRS will detect the object on exactly 15 tracks.

d. Find P1x Ú 152, the probability that SBIRS will detect the object on at least 15 tracks.

e. Find E1x2 and interpret the result.

*4.140 Emergency rescue vehicle use. An emergency rescue vehicle is used an average of 1.4 times daily. Use the Poisson distribution to find

a. The probability that the vehicle will be used exactly twice tomorrow

b. The probability that the vehicle will be used more than twice

c. The probability that the vehicle will be used exactly three times