Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

AP Statistics Help? 10 Points for Best Explanation!?

The Census Bureau reports that 27% of California residents are foreign born. Suppose that you choose three Californians independent of each other at at random. These are eight possible arrangements of foreign (F) and domestic (D) births. For example, FFD means that the first two are foreign born, and the third is not.

(a)Write down all eight arrangements and find the probability of each

(b) Let the random variable X be the number of foreign born people in each group of three Californians. WHat the the possible values of X? Use the probablities you found in (a) to construct a probability distribution table for X.

(c) What is the expected number of foreign born residents in a randomly selected group of three

(d) What is the standard deviation of X

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  • 9 years ago
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    a) FFF, FFD, FDF, DFF, DDF, DFD, FDD, DDD

    P(FFF)=(27/100)^3

    P(FFD)=P(FDF)=P(DFF)=(27/100)^2 * (73/100)

    P(DDF)=P(DFD)=P(FDD)=(27/100) * (73/100)^2

    P(DDD)=(73/100)^3

    b)X can be 0,1,2 or 3

    //the answers below can also be found using Bernoulli's formula

    P(X=0)=P(DDD)=(73/100)^3

    P(X=3)=P(FFF)=(27/100)^3

    P(X=2)=P(FFD)+P(FDF)+P(DFF)=3 * (27/100)^2 * (73/100)

    P(X=1)=P(DFD)+P(FDD)+P(DDF)=3 * (27/100) * (73/100)^2

    I hope you can construct the table using the data above

    c) E(X)= 0 * P(X=0) + 3 * P(X=3) + 2 * P(X=2) + 1 * P(X=1)

    //approximately 0.81

    d)the standard deviation is the square root of E(X^2)-(E(X))^2

    E(X^2)= 0 * 0 * P(X=0) + 3 * 3 * P(X=3) + 2 * 2 * P(X=2) + 1 * 1 * P(X=1)

    //approximately 1.24

    //therefore the standard deviation would be approximately 0.76

    Some of the calculations were done by hand, I would suggest redoing them yourself just to be sure

    Source(s): University course: Theory of probability and mathematical statistics
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