Random variable x represent the number of girls in a family of four children. 1) Construct a table describing the probability distribution, then find

Lewis Harvey

Lewis Harvey

Answered question

2020-11-01

The random variable x stands for the number of girls in a family of four children.
1) Build a table showing the probability distribution, then calculate the mean and standard deviation. (Hint: List the different possible outcomes.) 
2) Is it unusual for a family of four children to consist of four girls?

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2020-11-02Added 97 answers

1) The possibilities are (B=Boy and G=Girl): BBBB, BBBG, BBGB, BBGG, BGBB, BGBG, BGGB, BGGG, GBBB, GBBG, GBGB, GBGG, GGB, GGBG, GGGB, GGGG Every outcome has an equal chance. Let X be the number of girls: 
X - Probability 
0 - 0.0625 
1 - 0.25 
2 - 0.375 
3 - 0.25 
4 - 0.0625 
2) The average is the sum of the product x and the probabilities of x: 
μ=P(X)=00.625+10.25+20.375+30.25+40.0625=2 
The standard deviation is the square root of the sum of the squared deviations multiplied by the probability: 
σ=σ(xμ)2P(X)=(02)20.0625+...+(42)20.0625=2 
It is unusual to get 4 girls, because 4 is standard deviations from the mean. 
Result: μ=2, σ=1, Unusual

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