Question

The supplier is considering two changes to reduce to 1% the percentage of its large-cup lids that are too small. One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation of the lid diameters,

a. If the standard deviation remains at o = 0.02 inch, at what value should the supplier set the mean diameter of its large-cup lids so that only 1% are too small to fit?
b. If the mean diameter stays at = 3.98 inches, what value of the standard deviation will result in only 1% of lids that are too small to fit?
c. Which of the two options in parts (a) and (b) do you think is preferable?

Answer 1

To find the mean diameter and standard deviation for the sample, calculate the sample mean and sample standard deviation. Determine the values at which only 1% of the lids are too small. Compare the changes in the mean diameter and standard deviation to decide which option is preferable.

Step-by-step explanation:

a. To find the mean diameter and standard deviation for the sample, we need to calculate the sample mean and sample standard deviation. Let's assume the mean diameter of the large-cup lids is denoted by μ and the standard deviation is denoted by σ. We are given that the current standard deviation is σ = 0.02 inch.

To reduce the percentage of lids that are too small to 1%, we need to determine the values at which only 1% of the lids are too small.

b. Given that the mean diameter stays at μ = 3.98 inches, we need to find the value of the standard deviation that will result in only 1% of lids being too small to fit.

c. To determine which option is preferable, we need to compare the changes in the mean diameter and standard deviation to achieve the desired outcome.