SOLUTION: Let the random variable x represent the number of girls in a family with three children. The probability of a child being a girls in 0.36. Construct a table describing the probabil

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Question 1036225: Let the random variable x represent the number of girls in a family with three children. The probability of a child being a girls in 0.36. Construct a table describing the probability distribution, then find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of girls in a family with three children. Then the r.v. has pmf
p%28x%29+=+%28matrix%282%2C1%2C3%2Cx%29%29%2A0.64%5E%283-x%29%2A0.36%5Ex+=+0.262144, where x = 0,1,2,3.
p%280%29+=+%28matrix%282%2C1%2C3%2C0%29%29%2A0.64%5E3%2A0.36%5E0+=+0.262144
p%281%29+=+%28matrix%282%2C1%2C3%2C1%29%29%2A0.64%5E2%2A0.36%5E1+=+0.442368
p%282%29+=+%28matrix%282%2C1%2C3%2C2%29%29%2A0.64%5E1%2A0.36%5E2+=+0.248832
p%283%29+=+%28matrix%282%2C1%2C3%2C3%29%29%2A0.64%5E0%2A0.36%5E3+=+0.046656
Mean = mu+=+np+=+3%2A0.36+=+1.08 (Or practically, the mean number of girls in 3 children is 1, given the conditions.)
==>Standard deviation is sigma+=+sqrt%28npq%29+=+sqrt%283%2A0.36%2A0.64%29+=+0.83 to two significant figures.
Under the given condition (p = 0.36), it is unusual for a family of 3 children to consist of 3 girls (chance is only 4.7%.)