Respuesta :
Answer:
0.0013 probability that at least 6 employees were over 50.
Step-by-step explanation:
The employees were "chosen" to be dismissed without replacement, which means that the hypergeometric distribution is used to solve this question.
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]
In this problem:
8 employees dismissed means that [tex]n = 8[/tex]
Had 7 + 17 = 24 employees, which means that [tex]N = 24[/tex]
7 over 50, which means that [tex]k = 7[/tex]
What is the probability that at least 6 employees were over 50?
6 or 7, so:
[tex]P(X \geq 6) = P(X = 6) + P(X = 7)[/tex].
In which
[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 = 6) = h(6,24,8,7) = \frac{C_{7,6}*C_{17,2}}{C_{24,8}} = 0.0013[/tex]
[tex]P(X = 7) = h(7,24,8,7) = \frac{C_{7,7}*C_{17,1}}{C_{24,8}} \approx 0[/tex]
[tex]P(X \geq 6) = P(X = 6) + P(X = 7) = 0.0013 + 0 = 0.0013[/tex]
0.0013 probability that at least 6 employees were over 50.
