Specialty Toys, Inc., sells a variety of new and innovative children's toys. As with other products, Specialty faces the decision of how may Weather Teddy units to order for coming holiday season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000, 28,000 units. The wide range of order quantities suggested indicates considerable disagreement concerning the market potential. The product management team ask you for analysis of the stock-out probabilities for various order quantities, an estimate of the product potential, and to help make an order quantity recommendation. Specialty expects to sell Weather Teddy for $24 based on cost of $16 per unit. If inventory remains after the holiday season, Specialty will sell all surplus inventory for $5 per unit. After reviewing the sales history of similar products, Specialty%u2019s sales forecaster predicted and expected demand of 20,000 units with a .95 probability that demand would be between 10,000 units and 30,000 units. Prepare a managerial Report that addresses the following issues and recommends an order quantity for the Weather Teddy product. Use the sales forecaster’s prediction to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation. Compute the probability of a stock-out for the order quantities suggested by members of the management team. Compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales equal 10,000 units, most likely case in which sales equal 20,000 units, and best case in which sales equal 30,000 units. One of specialty’s manager felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only 30% chance of any stock-outs. What quantity would be order under this policy, and what is the projected profit under the three sales scenarios? Provide your own recommendations for an order quantity and note the associated profit projections. Provide a rationale for your recommendation.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Specialty Toys, Inc., sells a variety of new and innovative children's toys. As with other products, Specialty faces the decision of how may Weather Teddy units to order for coming holiday season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000, 28,000 units. The wide
- Use the sales forecaster’s prediction to describe a
normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation. - Compute the probability of a stock-out for the order quantities suggested by members of the management team.
- Compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales equal 10,000 units, most likely case in which sales equal 20,000 units, and best case in which sales equal 30,000 units.
- One of specialty’s manager felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only 30% chance of any stock-outs. What quantity would be order under this policy, and what is the projected profit under the three sales scenarios?
- Provide your own recommendations for an order quantity and note the associated profit projections. Provide a rationale for your recommendation.
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