HW 8 Q4
Having some trouble with question 4. Mine goes like this: Use normal approximation to estimate the probability of getting exactly 49 girls in 100 births. Assume that boys and girls are equally likely.
First I did:
E(X)=.5
E(S)=50
Var(x)=.5x.5=.25
Var(S)=.25x100=25
Std Dev=5
So my formula looks like:
Z=(49-50)/5, or -.2, which gives a probability of .4207. This was incorrect.
Then I remembered that to find the probability of an exact number, we had to figure out the probability of the numbers of either side of it. So I did:
Z=(48-50)/5= -.4 and Z=50-50)/5=0, giving me a Z value of -.4 and a probability of .3446. This was also wrong. Any ideas where I'm going astray?
Comments
To use a normal distribution to estimate the probability of getting exactly $k$ successes, you'll need to go from $k-1/2$ to $k+1/2$ or, in your case, from $48.5$ to $49.5$. Give that a try and let us know how it goes!
D'oh! That did it, thanks!