What is the Maximum Number of Pens in a Box to Ensure Quality?

How many pens can a company put in a box to maintain quality standards?

The company manufactures pens and sells them in boxes of 30. With 1% of the pens being defective, the company wants to ensure the probability of defective pens in a box is less than 40%. What is the maximum number of pens that can be placed in a box while maintaining quality assurance?

Maximum Number of Pens in a Box:

The maximum number of pens the company can put in a box to maintain quality standards is 105 pens. This ensures that the probability of having defective pens in a box is less than 40%.

Understanding Quality Assurance in Pen Manufacturing:

When a company manufactures pens and packages them in boxes, maintaining quality standards is crucial to customer satisfaction. In this scenario, where 1% of the pens are defective, the company must calculate the maximum number of pens in a box to prevent a high probability of receiving defective products.

The concept of binomial probability is utilized to determine the maximum number of pens that can be placed in a box while ensuring quality assurance. By recognizing the probability of one or more defective pens as the complement of the probability of zero defective pens, the company can set a threshold to prevent a high probability of defects in a box.

Calculating the maximum number of pens involves solving for 'n' in an inequality equation, where the probability of having defective pens in a box is less than 40%. By using the formula for binomial distribution and considering the 1% defect rate, the company determines that packing up to 105 pens in a box is the optimal choice to maintain quality standards.

By adhering to this maximum number of pens per box, the company ensures that customers receive high-quality products and minimizes the risk of receiving defective pens.