The demand for Carolina Industries' product varies greatly from month to month. Based on the past two years of data, the following probability distribution shows the company's monthly demand:
Unit Demand Probability
300 0.20
400 0.30
500 0.35
600 0.15
a. If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina's monthly order quanitity be for this product?
b. Assume that each unit will demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month if it places an order based on your answer to part (a) and the actual demand for thr the item 300 units?
10. Consider a binomial experiment with n = 10 and p = 0.10. Use the binomial tables (Appendix B) to the answer parts (a) through (d).
a. Find f(0).
b. Find f(2).
c. Find P(x < (less then or equal to symbol) 2).
d. Find P(x > (greater than or equal to) 1).
e. Find E(x).
f. Find Var(x) and o.
24. Probability : Demand for a Product
The demand for a product is estimated to be normally distributed with u=200 and o=40. Let x be the number of units demanded and find the following probabilities.
a. P(180< x <220)
b. P(x > 250)
c. P(x < 100)
d. P(225 < x < 250)
25. In 2003, the average stock price for companies making up the S&P 500 was $30, and the standard deviation was $8.20 (BusinessWeek, Special Annual Issue, Spring 2003). Assume the stock prices are normally distributed.
a. What is the probability that a company will have a stock price of at least $40?
b. What is the probability that a company will have a stock price no higher than $20?
c. How high does a stock price have to be to put a company in the top 10%?