A gender-selection technique is designed to increase the likelihood that a baby

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, 919 births consisted of 480 baby girls and 439 baby boys. In analyzing these results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 480480 girls in 919919 births.

b. Find the probability of getting 480480 or more girls in 919919 births. If boys and girls are equally likely, is 480480 girls in 919 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? a. The probability of getting exactly 480 girls in 919 births is

Explanation / Answer

p=probability of a girl=0.5

here we use binomial distribution with parameter n=919 and p=0.5 and for

Binomial distribution ,P(X=r)=nCrpr(1-p)n-r  

(a) P(X=480)=0.0106 ( using ms-excel command =BINOMDIST(480,919,0.5,0))

(b) P(X>480)=1-P(X<480)=1-0.9171=0.0829

P(X<480)=0.9171 (  using ms-excel command =BINOMDIST(480,919,0.5,1))

(c) result from part (b) is more relevent as its give the cumulative probability

(d) based on results P(X<480)=0.9171 , is technique is effective

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