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, 967 births consisted of 497 baby girls and 470 baby boys. In analyzing these results, assume that boys and girls are equally likely. a. Find the probability of getting exactly 497 girls in 967 births. b. Find the probability of getting 497 or more girls in 967 births. If boys and girls are equally likely, is 497 girls in 967 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 497 girls in 967 births is (Round to four decimal places as needed.)

Explanation / Answer

since boys are girsl are equally likely so each of probability will be= 1/2=0.5

here we use binomial distribution with paramter n=967 and p=0.5 and let r=number of girs then for

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

(a) P(X=497)=0.0176 ( using ms-excel command=BINOMDIST(497,967,0.5,0) )

(b) P(X>=497)=1-P(X<497)=1-0.816=0.194

(c) cumulative probability i.e. (b) is relevent

(d) based on result genender selection results is not effective at 5% level of significance using normal approximiation of binomial distribution.

(d)

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