Question

With a \( 0.09 \) percent chance of a stockout, what is the z-value to use in calculating safety stock? (Round your answer to two decimal points.) Use Table B.2

Answer 1

The z-value used for calculating safety stock with a 0.09 percent chance of a stockout is approximately 3.29, which corresponds to the 99.91 percent service level on a normal distribution curve.

Step-by-step explanation:

If we are looking to determine the z-value for calculating safety stock with a 0.09 percent chance of a stockout, we are essentially finding the z-score that corresponds to the desired service level in a normal distribution. In terms of area under the normal curve, a stockout chance of 0.09 percent implies a service level of 99.91 percent, meaning we want the area under the curve to the left of our z-value to be 0.9991.

Consulting a z-table or using a calculator, we find the z-score that corresponds to an area of 0.9991 to the left is approximately z = 3.29. Therefore, to maintain a safety stock level that has a 0.09 percent chance of a stockout, we should use a z-value of 3.29 in our calculations.

Answer 2

To calculate safety stock with a 0.09% chance of stockout, you refer to a standard normal distribution table to find the z-value that corresponds to a service level of 99.91%. The z-value that matches is approximately 3.08.

Step-by-step explanation:

When dealing with inventory management, particularly in setting levels for safety stock, the z-value is critical as it correlates to the desired service level, i.e., the probability of not having a stockout. A stockout chance of 0.09 percent translates to a service level of 99.91 percent (100% - 0.09%). To find the corresponding z-value, one would typically refer to a standard normal distribution table (Table B.2), which lists cumulative probabilities relative to z-values.

For a cumulative probability of 0.9991 (99.91%), the z-value that closely matches is found in the table. The exact z-value may not be 0.9991 due to the discrete nature of tables, but it will be the number closest to this value. Upon consulting a standard normal distribution table, a cumulative probability of 0.9991 corresponds to a z-value of approximately 3.08. Therefore, for a stockout chance of 0.09 percent, you would use a z-value of 3.08 to calculate safety stock.