Question

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 41​% of all employees believe their company president possesses low ethical standards. Suppose 20 of a​ company's employees are randomly and independently sampled. Assuming the​ paper's claim is​ correct, find the probability that more than eight but fewer than 12 of the 20 sampled believe the​ company's president possesses low ethical standards.

Answer 1

Answer:

P=0.3726 or 37.26%

Step-by-step explanation:

The success, with 41% of probability of occurring, is that the employee believes the ​ company's president possesses low ethical standards. For more than 8 and less than 12 successes, it means the probability of having  9, 10 or  11 successes (all these summed).

The formula is:

$b(x;n,p)= \ _nC_x*p^x*(1-p)^{n-x}$

Where x is the number of successes,n the number of trials, p the probability of success,$_nC_x$ refers to the combinations that can occur,  and it's formula is:

$_nC_x=\frac{n!}{x!(n-x)!}$

Calculating each case:

$b(9,20,0.41)=\frac{20!}{9!(20-9)!}*0.41^9*(1-0.41)^{20-9}=0.1658$

$b(10,20,0.41)=\frac{20!}{10!(20-10)!}*0.41^{10}*(1-0.41)^{20-10}=0.1267$

$b(11,20,0.41)=\frac{20!}{11!(20-11)!}*0.41^{11}*(1-0.41)^{20-11}=0.0801$

Adding each case:

$P=0.1658+0.1267+0.0801= 0.3726$