Question

In processed food, the standard plate count shall not exceed \(10^6/\text{g}\) or be higher than \(10^5/\text{g}\). In a 3 class microbiological sampling plan where \(n=5\), \(c=2\), \(m=10^5\), \(M=10^6\), which of the following statement(s) is/are true for 5 sample units (\(n=5\))?
A. The lot will be rejected if any sample unit exceeds a count of \(10^6/\text{g}\)
B. The lot will be rejected if three or more sample units exceed a count of \(10^5/\text{g}\)
C. The lot will be accepted if any two units have counts of less than \(10^6/\text{g}\)
Choose the correct answer from the options given below:

• A. A only
• B. B only
• C. A and B
• D. C only

Hint:

Remember the 3-class plan acceptance rules:
- Accept if: Zero units \({>} M\) AND at most \(c\) units are between \(m\) and \(M\).
- Reject if: Any unit \({>} M\) OR more than \(c\) units are between \(m\) and \(M\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A three-class microbiological sampling plan is used by food safety regulators (such as ICMSF/FSSAI) to assess food lots based on three categories of quality: acceptable, marginally acceptable, and unacceptable.

Step 2: Detailed Explanation:
Let us analyze the parameters of this 3-class plan:
- \(n = 5\): Number of sample units chosen randomly from the lot.
- \(m = 10^5/\text{g}\): The threshold value separating acceptable quality from marginally acceptable quality. Counts \(\le m\) are fully acceptable.
- \(M = 10^6/\text{g}\): The limit separating marginally acceptable from completely unacceptable quality. Any single value \({>} M\) is completely unacceptable.
- \(c = 2\): The maximum allowable number of marginally acceptable sample units (whose counts fall between \(m\) and \(M\)).
Let us evaluate the statements:
- Statement A: If any single sample unit has a count exceeding \(10^6/\text{g}\) (\(M\)), the lot is immediately and unconditionally rejected. Thus, Statement A is true.
- Statement B: We can tolerate at most \(c = 2\) units with counts greater than \(m = 10^5/\text{g}\) (but less than \(M\)). If three or more units exceed \(10^5/\text{g}\), the limit \(c\) is violated, and the entire lot is rejected. Thus, Statement B is true.
- Statement C: Accepting the lot depends on all 5 units meeting the criteria. Just having two units below \(10^6/\text{g}\) is insufficient if others exceed \(M\). Thus, Statement C is false.

Step 3: Final Answer:
Both statements A and B are true, which corresponds to option (C).