What is the probability that out of 125 babies born, at least 70 will be girls? Assume that boys and girls are equally probable, and round your answer to the nearest tenth of a percent. A.99.0% B.70.4% C.10.5% D.51.2%

Question

anonymous · Answer

10 20 30 40 50 60 70 / 80 90 100 110 120 ...125

70 / 50... Which I pick... B.

anonymous · Answer

By the way, I made up that way to get the answer, not a real technique.

amistre64 · Answer

im thinking it sounds like a binomial probability setup

anonymous · Answer

that what these are

amistre64 · Answer

125 C 70  times success^(70) times failure^(125-70)

125 C 70  (1/2)^(70)  (1/2)^(125-70)

soo:$$\sum_{k=70}^{125}\binom{125}{k}.5^{k}.5^{125-k}$$

amistre64 · Answer

or we can try a normal approximation :)

amistre64 · Answer

mean = np = 125(.5) = 62.5  so we would expect 62.5 of the population to be girls

sd = sqrt(npq) = sqrt(62.5*.5) = sqrt(31.25)

amistre64 · Answer

do you have to do this all by hand or do you have a ti83?

amistre64 · Answer

$$z=\frac{x-mean}{sd}$$
$$z=\frac{70-62.5}{\sqrt{31.25}}=1.34$$

looking on a ztable; that corresponds to about 100% - 91%

amistre64 · Answer

so yeah, it aint gonna be B, but it does look like it will be close to 10%