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Chapter 3: Q19E (page 170)

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

Expert verified

  1. 0.1


  2. No

Step by step solution

01

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,

P(Randomlyselectedchickenpassesinspectionwithfecalcontamination)=1100=0.01

Hence, the probability is 0.1.

02

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.

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Most popular questions from this chapter

On-the-job arrogance and task performance. Human Performance (Vol. 23, 2010) published the results of a study that found that arrogant workers are more likely to have poor performance ratings. Suppose that 15% of all full-time workers exhibit arrogant behaviors on the job and that 10% of all full-time workers will receive a poor performance rating. Also, assume that 5% of all full-time workers exhibit arrogant behaviors and receive a poor performance rating. Let A be the event that a full-time worker exhibits arrogant behavior. Let B be the event that a full-time worker will receive a poor performance rating.

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joint Rejectable

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a. What is the probability that the inspector judged the joint to be acceptable? That the committee judged the joint to be acceptable?

b. What is the probability that both the inspector and the committee judged the joint to be acceptable? That neither judged the joint to be acceptable?

c. What is the probability that the inspector and the committee disagreed? Agreed?

Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities:

P (E1) = .20, P (E2) = .30, P (E3)= .30, P (E4) = .10, P (E5) = .10.

a. Calculate P (A), P (B), and P (A∩B).

b. Suppose we know that event A has occurred, so that the reduced sample space consists of the three sample points in A—namely, E1, E2, and E3. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P (Ei/A)]. Verify that the conditional probabilities are in the same proportion to one another as the original sample point probabilities.

c. Calculate the conditional probabilityP (E1/A)in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection A∩B, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability:

P (B/A) =P (A∩B)P (A)

Verify that the two methods yield the same result.

d. Are events A and B independent? Why or why not?
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