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, 803 births consisted of 420 baby girls and 383 baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 420 girls in 803 births.

b. Find the probability of getting 420 or more girls in 803 births. If boys and girls are equally​ likely, is 420 girls in 803 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

for 803 births ; mean number of girl =np=803*0.5 =401.5

and std eviaiton =(np(1-p))^1/2 =14.169

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	401.5
std deviation   =σ=	14.169

probability of getting exactly 420 girls in 803 births:

probability =

P(419.5<X<420.5)

=

P(1.2704<Z<1.341)=

0.91-0.898=

0.0120

b)

probability of getting 420 or more girls in 803 births :

probability =

P(X>419.5)

=

P(Z>1.27)=

1-P(Z<1.27)=

1-0.898=

0.1020

c)the result from  part​ (b)  is​ effective

d)

as probability of that happening is not less than 0.05 threfore it is not unsuual event

therefore we cannot say that  the​ gender-selection technique is​ effective.