Question

Probability.

It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens.

Answer 1

Answer: 0.0386

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:

`P(X=x) = \ ^nC_x p^x(1-p)^(n-x)`

The probability that the consumer will have more than 6 contaminated chickens :-

`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`

`=0.03860084306\approx0.0386` (simplified)

Hence, the required probability = 0.0386