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.)&nbsp;2) Is it unusual for a family of four children to consist of four girls?

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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.)&amp;nbsp;2) Is it unusual for a family of four children to consist of four girls?

Demi-Leigh Barrera · Accepted Answer

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:&amp;nbsp;X - Probability&amp;nbsp;0 - 0.0625&amp;nbsp;1 - 0.25&amp;nbsp;2 - 0.375&amp;nbsp;3 - 0.25&amp;nbsp;4 - 0.0625&amp;nbsp;2) The average is the sum of the product x and the probabilities of x:&amp;nbsp;μ=∑P(X)=0∗0.625+1∗0.25+2∗0.375+3∗0.25+4∗0.0625=2&amp;nbsp;The standard deviation is the square root of the sum of the squared deviations multiplied by the probability:&amp;nbsp;σ=σ(x−μ)2P(X)=(0−2)2∗0.0625+...+(4−2)2∗0.0625=2&amp;nbsp;It is unusual to get 4 girls, because 4 is standard deviations from the mean.&amp;nbsp;Result:&amp;nbsp;μ=2,&amp;nbsp;σ=1,&amp;nbsp;Unusual

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

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