Respuesta :
Answer:
0.9167 = 91.67% probability that the entire batch will be accepted
Step-by-step explanation:
The CDs are chosen 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]
2100 write-rewrite CDs, and 60 are defective.
This means, respectively, that [tex]N = 2100, k = 60[/tex]
3 of these CDs are randomly selected for testing
This means that [tex]n = 3[/tex]
What is the probability that the entire batch will be accepted?
Probability of none defective, so P(X = 0).
[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 = 0) = h(0,2100,3,60) = \frac{C_{60,0}*C_{2040,3}}{C_{2100,3}} = 0.9167[/tex]
0.9167 = 91.67% probability that the entire batch will be accepted
