# Thread: Binomial probability question

1. here is another one...will appreciate any help ...

A recent article in the paper claims that business ethics are at an all-time low. reporting on a recent sample, the paper claims that 30% of all employees believe their company CEO has low ethical standards. Suppose 20 of a company's employees are randomly sampled. Assuming the paper's claim is correct, find the probability that more than 8 but fewer than 12 of the 20 sampled believe the company's CEO has low standards.

2. Well you know the probability and number or trials (n), so it's just a case of using the binomial distribution formula to calculate P(X=9) + P(X=10) + P(X=11). Are you able to find the answer now?

3. The binomial distribution formular i know is the one you helped on the other problem...I tried to use that but I dont get the solution. if you can help me more i will really appreciate....
Thanks

4. Hello Allenge
Originally Posted by Allenge
here is another one...will appreciate any help ...

A recent article in the paper claims that business ethics are at an all-time low. reporting on a recent sample, the paper claims that 30% of all employees believe their company CEO has low ethical standards. Suppose 20 of a company's employees are randomly sampled. Assuming the paper's claim is correct, find the probability that more than 8 but fewer than 12 of the 20 sampled believe the company's CEO has low standards.
The probability of 'success', $p = 0.3$, where a 'success' is that an individual employee chosen at random believes that the CEO has low standards. The probability of 'failure', $q = 0.7$. The experiment (choosing an employee and determining their views about the CEO) is repeated $n$ times, where $n = 20$.

The probability of $r$ successes out of $n$ is $\binom{n}{r}p^rq^{n-r}$

You need to calculate this probability when $n = 20$ and $r = 9, 10$ and $11$ in turn, and add these three results together.

If my working is correct, the answer is 0.1082 (4 d.p.)