Question

USDA chicken inspection. The U.S. Department of Agriculture (USDA) reports that one in every 100 slaughtered chickens passes inspection with fecal contamination under its standard inspection system.

a. If a slaughtered chicken is selected at random, what is the probability of passing inspection with fecal contamination?

b. The probability of part a was based on a USDA study that found that 306 of 32,075 chicken carcasses passed inspection with fecal contamination. Do you agree with the USDA's statement about the likelihood of a slaughtered chicken passing inspection with fecal contamination?

Short answer

1. 0.1

   
   

2. No

Step-by-step solution

Step-by-Step SolutionStep 1: The probability that it will pass fecal contamination inspection

Probability refers to the chance of a random event's outcome. This term refers to determining the likelihood of a given occurrence occurring.

Here,

Fecal contamination is detected in one out of every 100 slaughtered chickens.

Therefore,

$$\begin{gathered} \mathbf{P}\mathbf{(}\mathbf{Randomly}\mathbf{}\mathbf{selected}\mathbf{}\mathbf{chicken}\mathbf{}\mathbf{passes}\mathbf{}\mathbf{inspection}\mathbf{}\mathbf{with}\mathbf{}\mathbf{fecal}\mathbf{}\mathbf{contamination}\mathbf{)} \\ \mathbf{=}\frac{\mathbf{1}}{\mathbf{100}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{01} \end{gathered}$$

Hence, the probability is 0.1.

The USDA's statement that a slaughtered chicken with fecal contamination is unlikely to pass inspection

No, it's difficult to agree with the USDA's statement regarding the possibility of a slaughtered chicken passing inspection with fecal contamination. According to this research, just 1% of slaughtered chickens pass fecal contamination inspection, implying an extremely low success rate.

It means that 99% of the chickens slaughtered are infected, an unusually high proportion.