During 2010, the United States performed its every ten-year census. Suppose that

Question

During 2010, the United States performed its every ten-year census. Suppose that the Census every Bureau sampled (names generated by the computer, with replacement) 1000 residents of Massachusetts (population: 6,000,000) and asked them to fill out a more detailed census form. Let X = the number of people in this sample who live in the greater Boston (Massachusetts) area (population: 2,000,000). The (circle your answer and explain your choice): (a) X is a binomial random variable with n = 6,000,000 and theta = 1/3. X is not a binomial random variable since the events "Massachusetts resident" and (b) "greater Boston resident" are not independent. (c) X is a binomial random variable with n = 1000 and theta = 1/3. (d) X is not a binomial random variable because there are more than two outcomes with respect to where a person might live. (e) X is a binomial random variable with n = 1000 and theta = 1/6000.

Explanation / Answer

X is binomial random variable with n = 1000 , p =1/3

option C) is correct

as X is number of people in the sample of 1000 who live in Boston

so n = 1000

p = 1/3

because the probability of finding Boston people = 2000,000/6000,000 = 1/3

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