Question

Please provide answers for the questions a, b, c and d.

Thank You :)

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, 809 births consisted of 421 baby girls and 388 baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 421 girls in 809 births.

b. Find the probability of getting 421 or more girls in 809 births. If boys and girls are equally​ likely, is 421 girls in 809 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 expected number of girls =np=809*0.5=404.5

std deviation=sqrt(np(1-p))=14.221

therefore from normal distribution and continuity correction:

a) probability of getting exactly 421 girls in 809 births:

probability =

P(420.5<X<421.5)

=

P(1.13<Z<1.2)=

0.8849-0.8708=

0.0142

b)

probability of getting 421 or more girls in 809 births:

probability =

P(X>420.5)

=

P(Z>1.13)=

1-P(Z<1.13)=

1-0.8708=

0.1292

c)

from part b)

d)

as probability is not less than 0.05 ; threfore we can not say for sure that technique is effective