Question

it has been estimated that about 30% of frozen chicken 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

The probability that the consumer will have more than 6 contaminated chickens is 0.039.

The binomial distribution is a frequency distribution that shows how many successful outcomes there could be in a set number of trials with an equal chance of success. Given a success probability of "p" for each experiment trial, it shows the likelihood that an experiment will succeed "x" times out of "n" trials. The formula to calculate this binomial distribution is $P(X=x)= \;_nC_xp^x(1-p)^{n-x}$

Given the p=0.30 and n=12. Then, the required probability that the consumer will have more than 6 contaminated chickens is,

$\begin{aligned}P(X > 6)&= P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)+P(X=12)\\&=12C_7(0.3)^7(0.7)^5\cdots\cdots\cdots12C_{12}(0.3)^{12}(0.7)^{0}\\&=0.0386\\&=0.039\end{aligned}$

The required answer is 0.039.

To know more about binomial distribution:

https://brainly.com/question/29137961

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