Question

What is the probability that out of 125 babies born, at least 60 will be girls? Assume that boys and girls are equally probable.

(I got the answer 70.54 I just want to make sure I did it correctly, thanks!)

Answer 1

we can use the formula we used in the previous problem

Answer 2

we want probability 60 or greater

Answer 3

http://www.wolframalpha.com/input/?i=SUM_i%3D60^125+%28125+choose+i%29*1%2F2^125

Answer 4

ok thanks, what i did this time was i did 125(.5)= 62.5
sqrt(31.25)
then: z=60-62.5/sqrt(31.25)= -.4472135955 and then looked it up on the z score chart and thats how i got the answer

Answer 5

right, just make sure you know what type of z table it is
sometimes it uses P ( Z < a ) , sometimes it uses P ( Z > a)

if it is the latter, you will need to subtract by 1

Answer 6

ohh ok so is that where i messed up?

Answer 7

also this is where i got the table from http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

Answer 8

yes that table gives you P ( Z < a )

Answer 9

also you need to make a binomial continuity correction

Answer 10

we are going to find
P( X >= 59.5 ) , since X = 60 is a rectangle from 59.5 to 60.5

Answer 11

ok cool so do i just replace the 60 with 59.5 in the same equation?

Answer 12

yes, to find the z score

Answer 13

it turns out on calculator

normalcdf ( 60, 1E99, 125*.5 , sqrt( 125 * .5 * .5) ) = .6726 , which is wrong

Answer 14

thats why we need the 'binomial correction factor '

Answer 15

yea i replaced it at 59.5-62.5/5.59 and got 3/5.59= .5366726

Answer 16

that should be -.5367

Answer 17

and now
P( Z > -.5367) = 1 - P ( Z < -.5367) by complement rule

Answer 18

ok, so i shouldn't use the z-score table but ue the complement rule instead?

Answer 19

youre doing it correct

Answer 20

we just have to use complement rule, since the table only shows one direction

Answer 21

lets round -.5367 to -.54

P( Z < -.54) = .2981

now we want
P( Z > -.54)

but that is equal to

1 - P ( Z < -.54) = 1- .2946


this is only accurate to 2 decimal places i would say

Answer 22

ok so it is 70.54 then

Answer 23

isn't statistics fun :)

Answer 24

let me draw what we are doing

Answer 25

hahaha, that was the answer i got in the beginning!

Answer 26

yes