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,

813 births consisted of 414 baby girls and 399 baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 414 girls in 813 births.

b. Find the probability of getting 414 or more girls in 813 births. If boys and girls are equally​ likely, is 414 girls in 813 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

here mean of distribution=μ=np=		406.50
and standard deviation σ=sqrt(np(1-p))=		14.26
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

a()

probability of getting exactly 414 girls in 813 births:

probability =P(413.5<X<414.5)=P((413.5-406.5)/14.257)<Z<(414.5-406.5)/14.257)=P(0.49<Z<0.56)=0.7123-0.6879=0.0244

b)

probability =P(X>413.5)=P(Z>(413.5-406.5)/14.257)=P(Z>0.49)=1-P(Z<0.49)=1-0.6879=0.3121

c)

part b)

d)

No since it is not less than 0.05 level of significance