Question

If a store runs out of advertised material during a sale, customers become upset, and the store loses not only the sale but also goodwill. From past experience, a music store finds that the mean number of cds sold in a sale is 845, the standard deviation is 15, and a histogram of the demand is approximately normal. The manager is willing to accept a 2. 5% chance that a cd will be sold out. About how many cds should the manager order for an upcoming sale?.

Answer 1

The manager should order approximately 816 CDs for the upcoming sale.

Step-by-step explanation:

To determine how many CDs the manager should order for an upcoming sale, we can use the concept of z-scores and the normal distribution. Since the manager is willing to accept a 2.5% chance of a CD being sold out, we need to find the z-score corresponding to this probability. Using the z-score table or a calculator, we find that the z-score is approximately -1.96. The formula to calculate the order quantity is:

Order Quantity = Mean + (z-score * Standard Deviation)

Substituting the given values, we have:

Order Quantity = 845 + (-1.96 * 15) = 815.6

Therefore, the manager should order approximately 816 CDs for the upcoming sale.