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,

813 births consisted of 414 baby girls and 399 baby boys. In analyzing these results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 414 girls in 813 births.

b. Find the probability of getting 414 or more girls in 813 births. If boys and girls are equally likely, is 414 girls in 813 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 mean of distribution=μ=np= | 406.50 | |

and standard deviation σ=sqrt(np(1-p))= | 14.26 | |

for normal distribution z score =(X-μ)/σx |

therefore from normal approximation of binomial distribution and continuity correction: |

a()

probability of getting exactly 414 girls in 813 births:

probability
=P(413.5<X<414.5)=P((413.5-406.5)/14.257)<Z<(414.5-406.5)/14.257)=P(0.49<Z<0.56)=0.7123-0.6879=0.0244 |

b)

probability
=P(X>413.5)=P(Z>(413.5-406.5)/14.257)=P(Z>0.49)=1-P(Z<0.49)=1-0.6879=0.3121 |

c)

part b)

d)

No since it is not less than 0.05 level of significance

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