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, 994 births consisted of 521 baby girls and 473 baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 521 girls in 994 births.

b. Find the probability of getting 521 or more girls in 994 births. If boys and girls are equally​ likely, is 521 girls in 994 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) having boys and girls are equally likely which means that

probability of having a girl = probability of having a boy = p =0.5

the probability of getting exactly 521 girls in 994 births is binomial with probability of success p =0.5,

number of trials n = 994

b) Find the probability of getting 521 or more girls in 994 births.

= 6.8% (rounded to one decimal)

This probability is less than 7%

Hence having 521 girls in 994 births can be considered unusual high but not impossible

c) Result from part b is more acurate as getting the exact probability gives you less idea as the probability is too low.

if calculating a probability of having 521 or more birth (considering the natural phenominon that both are equally likely), the probability is high it only shows that the it is quite natural to have 521 girls or more of 994 births but if the probability is low than having 521 girls of 994 birth is quite unusual & treatment achieving that number tells that the treatment can be considred effective to increase the likelihood that a baby will be a girl.

d) Yes, it appear that the​ gender-selection technique is​ effective as the probability in part b is less than 7%.