Respuesta :
Using the hypergeometric distribution, there is a 0.2486 = 24.86% probability that the entire batch will be rejected.
What is the hypergeometric distribution formula?
The formula to find the hypergeometric distribution formula is
P(X=x)=P(x, N, n, K)[tex]=\frac{C_{k, x} C_{N-k, n-x} }{C_{N, n} }[/tex]
[tex]C_{n, x} =\frac{n!}{(n-x)!}[/tex]
The parameters are:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
For this problem, the values of the parameters are given as follows:
N = 8000, n = 7, k = 0.04 x 8000 = 320
The probability that the entire batch will be rejected is P(x≥1), given as follows: P(x≥1)=1-P(X=0)
In which,
P(X=0)=P(0, 8000, 7, 320)[tex]=\frac{C_{320, 0} C_{7680, 7} }{C_{8000, 320} }=0.7514[/tex]
Now, P(x≥1)=1-0.7514=0.2486
Therefore, 0.2486 = 24.86% probability that the entire batch will be rejected.
More can be learned about the hypergeometric distribution at
brainly.com/question/24826394
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