Answer: 0.34
Step-by-step explanation:
Given : The proportion of items in a shipment are known to be defective : p=0.08
Number of items selected = 5
By using binomial probability distribution formula, the probability of getting success in x trials is given by :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that at least one defective item will be observed in this sample will be :-
[tex]P(x\geq1)=1-P(x<1)\\\\=1-P(0)\\\\=1-^5C_0(0.08)^0(1-0.08)^{5}\\\\=1-(0.92)^5=0.3409184768\approx0.34[/tex]
Hence, the probability that at least one defective item will be observed in this sample is 0.34
