Question

A​ gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the​ gender-selection technique, 860 births consisted of 433 baby girls and 427 baby boys. In analyzing these​ results, assume that boys and girls are equally likely. a. Find the probability of getting exactly 433 girls in 860 births. b. Find the probability of getting 433 or more girls in 860 births. If boys and girls are equally​ likely, is 433 girls in 860 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

A) Find the probability of getting exactly 433 girls in 860 births.

Total Birth = 860 births.

Let, X be the number of girls birth.

In analyzing these​ results, assume that boys and girls are equally likely. Therefore,

The given proportion is 0.5.

OR you can also use excel command as,

=BINOMDIST(433,860,0.5,FALSE)

= 0.0266

The probability of getting exactly 433 girls in 860 births is 2.66%

B) Find the probability of getting 433 or more girls in 860 births. If boys and girls are equally​ likely, is 433 girls in 860 births unusually​ high?

Since the data is large enough, use the normal approximation:

The required probability is:

  

  

  

  

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)?

For the effectiveness of the given technique, the part-b probability is relevant because the technique is designed to increase the likelihood of a baby girl.

d. Based on the​ results, does it appear that the​ gender-selection technique is​ effective?

No, the gender-selection technique is not as effective as the probability in part-b (i.e. the birth of 433 or more girls) is less.