1.7) Some parts of California are particularly earthquake-prone. Suppose that in

Question

1.7) Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, the chance a homeowner is insured against an earthquake is 0.27. A sample of four homeowners are to be selected at random. Suppose X is a random variable that is modeled by a binomial distribution which describes the number homeowners out of the four that have earthquake insurance.

b) What is the most likely value for X?

c) What is the probability that at most 1 of the four selected have earthquake insurance? (Round your answer to four decimal places.)

d) What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.)

e) What is the expected value and standard deviation of X? (Round your answer to two decimal places.)
E(X)= x = ?
SD(X) = x = ?

Explanation / Answer

p = 0.27

n = 4

P(X = x) = 4Cx * 0.27x * (1 - 0.27)4-x

A) P(X = 0) = 4C0 * 0.270 * 0.734 = 0.2840

P(X = 1) = 4C1 * 0.271 * 0.733 = 0.4201

P(X = 2) = 4C2 * 0.272 * 0.732 = 0.2331

P(X = 3) = 4C3 * 0.273 * 0.731 = 0.0575

P(X = 4) = 4C4 * 0.274 * 0.730 = 0.0053

B) 1 is the most likely value for X

C) P(X < 1) = P(X = 0) + P(X = 1) = 0.2840 + 0.4201 = 0.7041

D) P(X > 2) = 1 - P(X < 2) = 1 - P(X < 1) = 1 - 0.7041 = 0.2959

E) E(X) = n * p = 4 * 0.27 = 1.08

SD (X) = sqrt(n * p * (1-p)) = sqrt(4 * 0.27 * 0.73) = 0.89

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