A country\'s government has devoted considerable funding to missile defense rese

Question

A country'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 0.6. Consider a sample of 10 simulated tracks, each with an intruding object. Let x equal the number of these tracks where SBIRS detects the object. Complete parts a through d. a. Give the values of p and n for the binomial distribution. p = (Round to one decimal place as needed.) n = b. Find P(x = 3), the probability that SBIRS will detect the object on exactly 3 tracks. P(x = 3) = (Round to three decimal places as needed.) c. Find P(x greaterthanorequalto 3), the probability that SBIRS will detect the object on at least 3 tracks. P(x greaterthanorequalto 3) = (Round to three decimal places as needed.) d. Find E(x) and interpret the result. A. E(x) = 6. For every 10 intruding objects, SBIRS will detect an average of 6. B. E(x) = 4. For every 10 intruding object, SBIRS will detect an average of 4. C. E(x) = 2.4. For every 10 intruding objects, SBIRS will detect an average of 2.4. D. E(x) = 3. For every 10 intruding objects, SBIRS will detect an average of 3. E. E(x) = 5. For every 10 intruding objects, SBIRS will detect an average of 5.

Explanation / Answer

a)

p = 0.6

n = 10

b)

p(X=x) = nCx px(1-p)n-x

p(X=3) = 10C3 0.63 0.47

           = 0.042

c)

p(x>=3) = 1-p(x<3)

            = 1-p(x<=2)

            = 1 - {p(x=0) + p(x=1) + p(x=2)}

            = 1 - { 10C0 0.60 0.410 + 10C1 0.61 0.49 + 10C2 0.62 0.48 }

            = 1 - (0.000105+0.00157+0.01062}

            = 0.988

d)

E(x) = np = 10*0.6 = 6

option A) is correct.

E(x) = 6, For every 10 intruding objects, SBIRS will detect an average of 6.

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