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 gender-selection technique, births consisted of 467 baby girls and 425 baby boys. In analyzing these results assume that boys and girls are equally likely a. Find the probability of getting exactly 467 girls in 892 births. b. Find the probability of getting 467 or more girls in 892 births. If boys and girls are equally likely, is 467 girls in 892 birth unusually high? c. Which probability is relevant for trying to determine whether the technique is effective, 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 467 girls in 892 births is (Round to four decimal places as needed.)

Explanation / Answer

x=467

n=892

p = x/n = 467 /892 =0.5235

mean =np =892*0.5235 =467

standard deviation =sqrt(np(1-p)

                                    =sqrt(892(0.5235(1-0.5235)

                                    =14.9167

probability of getting exactly 467 girls in 892 births

P(X=467)=P(467-0.5<X<467+0.5)       -continuity correction

                        =P(466.5 <X <467.5)

                        =P((466.5-467)/14.9167 <Z < (467.5-467)/14.9167)

                        =P(-0.0335 < Z < 0.0335)

                        = P(Z<0.0335) –P(Z<-0.0335)

                        =NORMSDIST(0.0335)- NORMSDIST(-0.0335)         -from the excel

                        =0.5134 -0.4866

                        =0.0268

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