Statistics test

Question

The Census Bureau reports that 27% of California residents were born outside the Untied States. Suppose that you choose four Californians independent of each other and at random. Let F = the number of foreign-born people in a randomly-selected group of four.

find the value of F

find the standard deviation of F

Answer 1

Since F is the number of foreign born people in a randomly selected group of four, F can take on discrete values between 0 to 4, inclusive. In other words, F is the set of numbers {0, 1, 2, 3, 4}

F happens to be a binomial variable since it meets the four criteria of a binomial distribution.

Formulas for binomial variables

Mean = np = 4(.27) = 1.08....which means we would expect that 1.08 people in a random group of four Californians would be foreign born.

Standard deviation = square root of (npq) = sqrt(4*.27*.73)=0.8879 people