Respuesta :
Answer:
0.2384 = 23.84% probability that 2 of the selected customers are financial services firms
Step-by-step explanation:
The customers are chosen from a sample without replacement, which means that the hypergeometric distribution is used.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
20 new customers have signed up for a specialized service your company provides.
This means that [tex]N = 20[/tex]
Twelve are financial services firms.
This means that [tex]k = 12[/tex]
Sample of 5
This means that [tex]n = 5[/tex]
What is the probability that 2 of the selected customers are financial services firms
This is P(X = 2).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,20,5,12) = \frac{C_{12,2}*C_{8,3}}{C_{20,5}} = 0.2384[/tex]
0.2384 = 23.84% probability that 2 of the selected customers are financial services firms
