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, 803 births consisted of 420 baby girls and 383 baby boys. In analyzing these results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 420 girls in 803 births.

b. Find the probability of getting 420 or more girls in 803 births. If boys and girls are equally likely, is 420 girls in 803 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?

Explanation / Answer

for 803 births ; mean number of girl =np=803*0.5 =401.5

and std eviaiton =(np(1-p))1/2 =14.169

a)

probability of getting exactly 420 girls in 803 births:

b)

probability of getting 420 or more girls in 803 births :

c)the result from  part (b)  is effective

d)

as probability of that happening is not less than 0.05 threfore it is not unsuual event

therefore we cannot say that  the gender-selection technique is effective.

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