Find the mean, variance, and standard deviation

[KatieLynn]

Homework Statement

If there are 4 children in a family, find the probability of getting exactly 3 girls. Find the mean, variance, and standard deviation. Use two different methods(binomial distribution method and general probability distribution method).

Homework Equations

Binomial distribution equations:
Mean=np
variance=npq
standard deviation= sq. root of variance

The Attempt at a Solution

mean= (4)(.75)=3

variance=(4)(.75)(.25)=.75

s.d.= .866

is that right?

 

[statdad]

Not quite - this is a guess, but you are using the value of $$0.75$$ as p because out of the four children, three are girls? If so, that's not correct.

With the information you are given you can only assume that

1. Births of boys and girls are independent
2. The probability a boy is born is $$0.50$$ and the probability a girl is born is $$0.50$$

Your method of calculation to find the mean, variance, and standard deviation are correct, but the value of $$p$$ isn't (as pointed out above)

You can use the formula

$$p(x) = C(4,x) p^x (1-p)^{4-x}$$

to find the probability of exactly three girls with the binomial distribution.

For the "fundamental principles" piece: write down all possible ways for there to be four children, and use basic principles of equally likely outcomes.