Question

If the standard deviation remains at σ = 0.02 inch, at what value should the supplier set the mean diameter of its large-cup lids so that only 1 re too small to fit?

Answer 1

To ensure that only 1 lid out of every 1,000 will be too small to fit, the supplier should set the mean diameter of its large-cup lids at -0.08 inch.

Step-by-step explanation:

To determine the value at which the supplier should set the mean diameter of its large-cup lids, we need to use the concept of z-scores. The formula for calculating the z-score is: z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. In this case, the z-score of -3 indicates that the desired value should be 3 standard deviations below the mean.

Using the z-score formula, we have: z = (-0.02 - μ) / 0.02. Solving for μ, we get: μ = -0.02 - (3 * 0.02) = -0.08 inch.

Therefore, the supplier should set the mean diameter of its large-cup lids at -0.08 inch, so that only 1 lid out of every 1,000 will be too small to fit.