4. After a large scale earthquake it is predicted that 30% of all buildings have

Question

4. After a large scale earthquake it is predicted that 30% of all buildings have been structurally compromised. a. What is the probability that if engineers inspect 10 buildings they will find exactly one that is b. What is the probability that if engineers inspect 10 buildings they will find less than or equal to 2 c. What is the probability that if engineers inspect 10 buildings they will find greater than 4 that are d. What is the expected number of buildings that an engineer will find structurally compromised if structurally compromised? that are structurally compromised? structurally compromised? the engineer inspects 10 buildings?

Explanation / Answer

This is a binomial distribution problem with probability of succes p = 0.3

P(X = k) = ncr * pk * (1-p)(n-k)

a) P(X = 1) = 10c1 * 0.3 * 0.79 = 0.12106

b) P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.710 + 10c1 * 0.3 * 0.79 + 10c2 * 0.32 * 0.78 = 0.382783

c) P(X > 4) = 1 - P(X <= 3) = 1 - 0.382783 - P(X = 3) = 1 - 0.382783 - 10c3 * 0.33 * 0.77 = 0.350389

d) Mean = np = 10*0.3 = 3 buildings

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