Final answer:
The question involves inventory management but lacks sufficient information to calculate recommended order quantity and safety stock. The stock-out probability for a given reorder point can be calculated using normal distribution, though the annual stock-out frequency requires more information about order cycle length.
Step-by-step explanation:
The student's question deals with inventory management concepts, mainly the calculation of order quantity, safety stock, and the probability of a stock-out based on the parameters of a normal distribution for lead-time demand. The recommended order quantity can be calculated using Economic Order Quantity (EOQ) formula, but the required parameters for this are missing in the question. For the safety stock and reorder point, typically the service level along with the lead-time demand distribution would be used. However, the information provided doesn't include a service level, so we cannot calculate the safety stock with the given data.
As for part (c), the normal probability distribution information provided (μ=25, σ=5) allows for the calculation of stock-out probability when the reorder point is set at 30 units. This can be found using standard normal distribution tables or a statistical software.
The probability of stock-out during the year can be derived by considering how frequently the order cycle occurs relative to the calculated probability of a stock-out per cycle. Without the order cycle length, we cannot provide this information.