Answer: 0.0386
Step-by-step explanation:
Given: The probability hat the frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked : p= 0.30
Sample size : n = 12
Let x = Number of contaminated chickens
Here , two outcomes for any chicken (either contaminated or not) , so it follows binomial distribution.
Binomial probability formula:
[tex]P(X=x) = \ ^nC_x p^x(1-p)^{n-x}[/tex]
The probability that the consumer will have more than 6 contaminated chickens :-
[tex]P(X>6)=P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)+P(X=12)\\\\=^{12}C_6(0.3)^6(0.7)^6+^{12}C_7(0.3)^7(0.7)^5+^{12}C_8(0.3)^8(0.7)^4+^{12}C_9(0.3)^9(0.7)^3+^{12}C_{10}(0.3)^{10}(0.7)^2+^{12}C_{11}(0.3)^{11}(0.7)^1+^{12}C_0(0.3)^{12}(0.7)^0[/tex]
[tex]=0.03860084306\approx0.0386[/tex] (simplified)
Hence, the required probability = 0.0386
