# Thread: Having a little difficulty

1. ## Having a little difficulty

Suppose it is known that 10% of the citizens of the United States are in favor of increased foreign aid. A random sample of 100 U.S. citizens is questioned on this issue. Find the mean and standard deviation of x, the number of citizens who favor increased foreign aid.

2. Originally Posted by bombo31
Suppose it is known that 10% of the citizens of the United States are in favor of increased foreign aid. A random sample of 100 U.S. citizens is questioned on this issue. Find the mean and standard deviation of x, the number of citizens who favor increased foreign aid.
In the sample of 100 the is a 10% chance for each citizen that they are
in favour on increased aid, so the number in favour in the sample of 100
has a binomial distribution with single case probability of a favourable outcome
equal to $\displaystyle p=0.1$.

For a sample of size N the mean number of successes is:

$\displaystyle \mu=N\times p$,

and the standard deviation is:

$\displaystyle \sigma=\sqrt{N \times p \times (1-p)}$.

So now just plug $\displaystyle N=100$ and $\displaystyle p=0.1$ into
these equations to find the answerers.

RonL

3. Thanks.I had done that then I worked out the probability. I then looked in the probability table but was unable to figure out how many favor increased aid. I got 4%. Probability was 3.33. I then checked the table. That number represented 0.9996. As probability was more than 1, I subtracted 0.9996 from 1 and got 0.0004. I am therefore assuming that it is then 4% of 100 which translates to 4 people. Please let me know if I am on the right track.
Gracias.

4. Originally Posted by bombo31
Thanks.I had done that then I worked out the probability. I then looked in the probability table but was unable to figure out how many favor increased aid. I got 4%. Probability was 3.33. I then checked the table. That number represented 0.9996. As probability was more than 1, I subtracted 0.9996 from 1 and got 0.0004. I am therefore assuming that it is then 4% of 100 which translates to 4 people. Please let me know if I am on the right track.
Gracias.
I am not a master of probability, but I see three things that you have done that are way off.

1. The problem already told you 10% favor increased aid.

2. $\displaystyle 1$%$\displaystyle =0.01=\frac{1}{100}$ so $\displaystyle 0.0004=0.04$%$\displaystyle \neq 4$%

3. Where did you get 3.33?

on a side note, NEVER ASSUME ANYTHING IN MATH! (or hacker might drill you)