Question

In a canning industry, the total process time (F0) was calculated as 3 min. If each can contains 20 spores having decimal reduction time of 1.6 min, the probability of spoilage would be ________ in 100 cans (round off to the nearest integer).

Hint:

The probability of spoilage in cans can be calculated using the D-value and total process time. The higher the process time relative to the D-value, the higher the probability of spoilage.

Answer 1

Correct Answer: 25

The decimal reduction time (D-value) is the time required to reduce the number of viable spores by 90%. Given that the total process time is 3 minutes and each can has 20 spores, we can calculate the number of viable spores remaining using the formula: \[ \text{Probability of spoilage} = 1 - 10^{-\frac{\text{Process time}}{\text{Decimal reduction time}}} \] Substituting the values: \[ \text{Probability of spoilage} = 1 - 10^{-\frac{3}{1.6}} = 1 - 10^{-1.875} = 1 - 0.013 \approx 0.987. \] Thus, the probability of spoilage in each can is approximately 0.987. For 100 cans, the expected number of spoiled cans is: \[ 0.987 \times 100 \approx 99. \] Thus, the probability of spoilage in 100 cans is approximately 28.