In Exercises, assume that 400 births are randomly selected. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected.
Exactly 205 girls.
Step 1 of 5</p>
you have to consider that there are so many possibilities from 0 girls to 400 girls. of course (assuming boys/girls are equally likely), around 200 girls will be the highest probability zone, but "exactly" 205 makes it unlikely.
Step 2 of 5</p>
Random Variable: X = # of girls in 400 births.
X is a Binomial Random Variable. Normal Approximation to Binomial?.
Assume p = 0.5; n = 400; q = 0.5.
n.p = n.q = 200 ≥ 5. (It is Ok to use the Normal approximation)
Step 3 of 5</p>
Find µ and σ for the Normal distribution.
For a Binomial Random Variable:
µ = n.p = 400(0.5)=200
σ = = = 100