Question

A popular ballpoint pen manufacturer reports that approximately 13% of all pens manufactured in their factory are defective. Use this information to answer the questions that follow. A. A stationary store ordered 250 ballpoint pens, how many should they expect will be defective? Round to one decimal place. Do not forget units. μ= B. What is the standard deviation of the distribution from A? Round to one decimal place. Do not forget units. σ= C. Based on the mean and standard deviation (parts A and B), what values of "r" would be considered unusual? Fill in the inequalities with the correct r value. r≤ ___and r≥___

Answer 1

The stationary store should expect 32.5 defective pens from an order of 250. The standard deviation is approximately 5.3 pens. Unusual values (r) would be considered if r≤ 21.9 pens or r≥ 43.1 pens.

Step-by-step explanation:

To calculate the expected number of defective pens from the stationary store order of 250 pens, we use the given defect rate of 13%. The expected number (mean) μ, is calculated as follows:

μ = Total P ens × Defect Rate = 250 pens × 0.13 = 32.5 pens

Hence, the store should expect approximately 32.5, or rounded to one decimal place, 32.5 defective pens.

To find the standard deviation σ of the distribution, we use the formula for the standard deviation of a binomial distribution:

σ = √(npq) = √(250 × 0.13 × (1 - 0.13)) = √(250 × 0.13 × 0.87) = √(27.825) ≈ 5.3 pens

Therefore, the standard deviation σ is approximately 5.3 pens.

Regarding part C, a value is usually considered unusual if it is more than two standard deviations from the mean. This would mean:

r ≤ μ - 2σ = 32.5 - (2× 5.3) = 21.9 pens

and

r ≥ μ + 2σ = 32.5 + (2× 5.3) = 43.1 pens