# Continuous Probability

• Oct 18th 2009, 07:43 PM
jas213
Continuous Probability
Continuous Probability Distributions- Statistics can someone solve the below problem?

Specialty faces the decision of how many Weather Teddy units to order fr the coming season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000 or 28,000 units. The wide range of order quantities suggested indicate considerable disagreement concerning the market potential. The product management team ask you for an analysis of the stock out probabilities for various order quantities, an estimate of the profit potential and to help make an order quanity recommendation. Specialty expects to sell weather teddy for \$24 based on a 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 f similar products, Specialty's senior sales forecaster predicted an expected demand of 20,000 units with .90 probability that demand would be between 10,000 units and 30,000 units.

1. use the sale 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

2. compute the probability of a stock out for the order quantities suggested by members f the management team.

3. compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales=10,000 units , most likely case in which sales =20,000 units and best case in which sales = 30,000 units.

4. one of specialty's managers felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 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?

5. Provide your own reccommendation for an order quantity and note the associated profit projections. Provide a rationale for your recommendation
• Oct 18th 2009, 11:22 PM
CaptainBlack
Quote:

Originally Posted by jas213
Continuous Probability Distributions- Statistics can someone solve the below problem?

Specialty faces the decision of how many Weather Teddy units to order fr the coming season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000 or 28,000 units. The wide range of order quantities suggested indicate considerable disagreement concerning the market potential. The product management team ask you for an analysis of the stock out probabilities for various order quantities, an estimate of the profit potential and to help make an order quanity recommendation. Specialty expects to sell weather teddy for \$24 based on a 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 f similar products, Specialty's senior sales forecaster predicted an expected demand of 20,000 units with .90 probability that demand would be between 10,000 units and 30,000 units.

1. use the sale 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

You need to find a normal distribution such that the mean is 20000 and 90% of the distribution falls into the interval 10000-30000.

A 90% interval for the normal distribtion is mean+/-1.645*SD, which with the above data will allow you to find the required mean and SD.

CB
• Oct 19th 2009, 06:04 AM
jas213
sorry it should be 95% in the question and captain i aint understand where you got that .829 from . how did you calculate that? can you work out the entire qustion one for me please? because i dont understand
• Oct 19th 2009, 07:56 AM
CaptainBlack
Quote:

Originally Posted by jas213
sorry it should be 95% in the question and captain i aint understand where you got that .829 from . how did you calculate that? can you work out the entire qustion one for me please? because i dont understand

First the 0.829 is a typo it should be 1.645.

a 95% probability changes the +/-1.645 to +/-1.960.

You get these by looking up the relevant probability P=1-(1-0.95)/2 in a table of the cumulative normal distribution (reverse look up in fact).

We are given mean=20000, then as 30000=20000+1.960*SD we find:

SD=10000/1.960.

So you have a demand distribution N(20000,(10000/1.960)^2)

CB
• Oct 19th 2009, 08:08 AM
jas213
ok. thanks alot now i see . But can you also help me with questions 3 and 4 please? Ill greatly appreciate it. cuz they the only two am stuck on now
• Oct 21st 2009, 12:10 PM
smurfy100
probability
Captain - how would i start solving the probability question - number 2? How does that question differ than number 4?