Question

What is the probability that out of 250 babies born, 110 or fewer will be boys? Assume that boys and girls are equally probable.

Answer 1

Let p=probability of success (a boy born)
probability remain constant over the 250 trials, and each trial is either success or failure (Bernoulli trial), so use the binomial distribution, n=250, p=0.5, and calculate P(X<=110).
where \(P(X=r)=\large (^{250}_r)p^r(1-p)^{n-r}\)
This will involve a large number (110) of summations. If you have a binomial distribution table, or have access to software that evaluates the cdf of the binomial distribution, you can do so.
Most people would (especially in exams) approximate the result with a normal distribution when there is a large number of trials, and the probability curve is symmetrical (p=0.5 is favourable). Do not forget the continuity correction.

Answer 2

ok i have a calculator that calculates the normalcdf

Answer 3

and the binomial cdc

Answer 4

Good, make sure you calculate the cdf.

Answer 5

What do you get?

Answer 6

somehow i got 5.52

Answer 7

Watch out! Probabilities cannot exceed 1!

Answer 8

cdf's always range between 0 and 1

Answer 9

yea i messed up i just don't know where, i entered trials: 250, p: 0.5, and left the x value blank and pressed enter and thats what came up

Answer 10

Your x value is what?

Answer 11

110?

Answer 12

I should say "what do you think X should be?"

Answer 13

Yep!
Put that in and see if the calculator behaves!

Answer 14

110

Answer 15

ok i got 3.3%

Answer 16

3.321% right?

Answer 17

yes

Answer 18

thankss!

Answer 19

You're welcome! :)

Answer 20

Couldn't spell right! sigh!


\(\bbox [10pt, yellow, border:5pt solid brown]{\Large \color{red}{ Awesome!...}}\)

Answer 21

hahaha(:

Answer 22

@hockeychick23
By the way, does your school/uni limt the kind of calculator you use in exams? If yes, is your calculator one of the approved ones?
Otherwise you need to practise normal approximation to binomial... just in case.

Answer 23

no it doesn't and yep my calculator is approved

Answer 24

Perfect, good for you!