Question

A. find the probability of getting exactly 472472 girls in 934934 births.
b. find the probability of getting 472472 or more girls in 934934 births. if boys and girls are equally​ likely, is 472472 girls in 934934 births unusually​ high?
c. which probability is relevant for trying to determine whether the technique is​ effective: the result from part​ (a) or the result from part​ (b)?
d. based on the​ results, does it appear that the​ gender-selection technique is​ effective?

Answer 1

Not sure what is meant by "technique" here. Likely some information was left out of the question.

But if we assume there's a $\dfrac12$ probability of a girl being born, then

$\mathbb P(X=472)=\dbinom{934}{472}\left(\dfrac12\right)^{472}\left(1-\dfrac12\right)^{934-472}\approx0.0247$

$\mathbb P(X\ge472)=\displaystyle\sum_{x=472}^{934}\binom{934}x\left(\dfrac12\right)^x\left(1-\dfrac12\right)^{934-x}\approx0.3842$