Respuesta :
Answer:
[tex]p(x\geq 1)=0.1975[/tex]
Step-by-step explanation:
the probability that x iPads are defective in the sample follows a hypergeometric distribution, so it is calculated as:
[tex]p(x)=\frac{kCx*((N-k)C(n-x))}{NCn}[/tex]
Where [tex]aCb=\frac{a!}{b!(a-b)!}[/tex]
Because we have a N elements with k elements that are defective and we are going to take a sample of n elements. So, replacing N by 100, k by 7 and n by 3, we get:
[tex]p(x)=\frac{7Cx*((100-7)C(3-x))}{100C3}[/tex]
Now, the probability of rejecting the shipment is the probability that at least one iPad of the sample is defective, so:
[tex]p(x\geq 1)=p(1)+p(2)+p(3)[/tex]
Then:
[tex]p(1)=\frac{7C1*((100-7)C(3-1))}{100C3}=0.1852\\p(2)=\frac{7C2*((100-7)C(3-2))}{100C3}=0.0121\\p(3)=\frac{7C3*((100-7)C(3-3))}{100C3}=0.0002[/tex]
Finally, the probability of rejecting the shipment is:
[tex]p(x\geq 1)=0.1852+0.0121+0.0002=0.1975[/tex]
