Final answer:
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