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 20 simulated tracks, each with an intruding object. Let x equal the number of these tracks on which SBIRS detects the object. (a) Is x (approximately) a binomial random variable? Group of answer choices No Yes

Answer 1

Answer: Yes

Explanation:

Given that :

Probability of success (p) = 0.8

Number of simulations (n) = 20

Number of tracks on which infrared system detects object = x

To test if it is binomial random variable :

For a binomial distribution :

P(x) = nCx * p^x * (1 - p)^(n-x)

Since the variables given are enough to create and use a binomial probability distribution, then x is approximately a binomial random variable.