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,

831831

births consisted of

426426

baby girls and

405405

baby boys. In analyzing these​ results, assume that boys and girls are equally likely.a. Find the probability of getting exactly

426426

girls in

831831

births.b. Find the probability of getting

426426

or more girls in

831831

births. If boys and girls are equally​ likely, is

426426

girls in

831831

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

426426

girls in

831831

births is

nothing .

​(Round to four decimal places as​ needed.)

b.

The

probability of getting

426426

or more girls in

831831

births is

nothing .

​(Round to four decimal places as​ needed.)

If boys and girls are equally​ likely, is

426426

girls in

831831

births unusually​ high?

A.

​Yes, because

426426

girls in

831831

births is far from what is​ expected, given the probability of having a girl or a boy.

B.

​Yes, because

426426

girls in

831831

births is not far from what is​ expected, given the probability of having a girl or a boy.

C.

​No, because

426426

girls in

831831

births is far from what is​ expected, given the probability of having a girl or a boy.

D.

​No, because

426426

girls in

831831

births is not far from what is​ expected, given the probability of having a girl or a boy.

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)?

A.

The results from part​ (a) and part​ (b) are​ equal, so they are equally relevant.

B.

The result from part​ (b) is more​ relevant, because one wants the probability of a result that is at least as extreme as the one obtained.

C.

Neither of the results are relevant.

D.

The result from part​ (a) is more​ relevant, because one wants the probability of a result that is exactly equal to the one obtained.

d. Based on the​ results, does it appear that the​ gender-selection technique is​ effective?

A.

YesYes​,

because the probability of having

426426

or more girls in

831831

births

isnbsp not nbsp not ​unlikely,

and​ thus,

isnbsp not nbsp not attributable

to random chance.

B.

YesYes​,

because the probability of having

426426

or more girls in

831831

births

isnbsp ​unlikely,

and​ thus,

isnbsp not nbsp not attributable

to random chance.

C.

NoNo​,

because the probability of having

426426

or more girls in

831831

births

isnbsp ​unlikely,

and​ thus,

isnbsp attributable

to random chance.

D.

NoNo​,

because the probability of having

426426

or more girls in

831831

births

isnbsp not nbsp not ​unlikely,

and​ thus,

isnbsp attributable

to random chance.

        More

                                                        Less

Click to select your answer(s).

0% SCORE:0REMAINING:10/10

Answer 1

Let X be the number of girls in 831 children. Then X ~ Binomial(n = 831, p = 0.5) if we assume that boys and girls are equally likely.

Using Normal approximation to the Binomial theorem, X follows Normal distribution with mean = np = 831 * 0.5 = 415.5 and standard deviation of = 14.41354

Probability of getting exactly 426 girls in 831 births = P(X = 426) =

= P(425.5 < X < 426.5) (Using Continuity correction)

= P( X < 426.5) - P(X < 425.5)

= P[Z < (426.5 - 415.5)/14.41354] -  P[Z < (425.5 - 415.5)/14.41354]

= P[Z < 0.7632] - P[Z < 0.6938]

= 0.7773 - 0.7561

= 0.0212

Probability of getting more than 426 girls in 831 births = P(X 426) =

= P(X < 425.5) (Using Continuity correction)

= P(X > 425.5)

= P[Z > (425.5 - 415.5)/14.41354]

= P[Z > 0.6938]

= 0.2439

If boys and girls are equally​ likely, is

D.

​No, because 426 girls in 831 births is not far from what is​ expected, given the probability of having a girl or a boy.

c.

The relevant effective probability is,

B.

The result from part​ (b) is more​ relevant, because one wants the probability of a result that is at least as extreme as the one obtained.

d.

Based on the​ results, it does not appear that the​ gender-selection technique is​ effective, because the Probability of getting more than 426 girls in 831 births is not very low.

D.

No, because the probability of having 426 or more girls in 831 births is not ​unlikely, and​ thus, is attributable

to random chance.