Question

Do the following problems: and for a product of Carolina Industries varies greatly from month to month. Based on the past two years of data, the following shows the monthly demand at Carolina Industries Unit Demand #Months 300 400 500 600 a. If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina's monthly order quantity be for this product? b. What are the variance and the standard deviation for the number of units demanded? 2. Military Radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack. Answer the following questions using the Binomial probability distribution. a. What is the probability that I detection system will detect an attack? D. 12 detection systems are installed in the same area and operate independently, hat is the probability that at least 1 of the systems will detect the attack? detect the attack? sems are installed, what is the probability that at least 1 of the systems will d. Would you recommend that recommend that multiple detection systems be operated? Explain. 3. The average stock price for company standard deviation is $8.20. Assume the stock p ock price for companies making up the S&P 500 is $30, and the 58.20. Assume the stock prices are normally distributed. probability a company will have a stock price of at least What is the probability a company b. What is the probability a company 6. How high does a stock price have to y a company will have a stock price no higher than $207 ce have to be to put a company in the top 10%

Answer 1

Answer :

(1).

(a).

Demand (x)	Relative probability	x* P(x)	x^2 * P(x)
300	4/(4+6+9+5) = 1/6	50	15000
400	6/(4+6+9+5) = 1/4	100	40000
500	9/(4+6+9+5) =3/8	187.5	93750
600	5/(4+6+9+5) = 5/24	125	75000

Carolina monthly order = Summation of x*P(x) = 50 + 100 + 187.5 + 125 = 462.5

(b). Variance = (Summation of x^2*P(x)) - [Summation of x*P(x))^2

= (15000 + 40000 + 93750 + 75000) - (462.5)^2

= 9843.75

Standard deviation = sqrt(variance) = sqrt(9843.75 = 99.21

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