Question

Consider a company that has two different divisions. The annual profits from the two divisions are independent and have distributions Profit1 ~ N(5, 32) and Profit2 ~ N(7, 42) respectively. Both the profits are in $ Million. Answer the following questions about the total profit of the company in Rupees. Assume that $1 = Rs. 45
A. Specify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company.
B. Specify the 5th percentile of profit (in Rupees) for the company
C. Which of the two divisions has a larger probability of making a loss in a given year?

Answer 1

Step-by-step explanation:

Consider a company that has two different divisions. The annual profits from the two divisions are independent and have distributions Profit1 ~ N(5, 3^2) and Profit2 ~ N(7, 4^2) respectively. Both the profits are in $ Million. Answer the following questions about the total profit of the company in Rupees. Assume that $1 = Rs. 45 A. Specify a Rup…

Answer 2

Answer:

Mean Profit of Company in rupees = 12 * 45 = 540 Million  

Step-by-step explanation:

Answer:-

Diivision1 = Profit1 ~ N (5, 32) = N (Ẋ1=5, S1 2= 32) , Division2 = Profit2 ~ N (7, 42) = N (Ẋ2=7, S22 = 42)

µ = Company = (Profit1 + Profit2) = Mean Profit of Diivision1 + Division2

                                                         = 5 + 7 = 12

Specify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company.

Ans :- Specify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company.

Variance of the Company Distribution =σ^2 = 32 + 42 = 9 + 16 = 25 = 52

Standard Deviation of the Company Distribution =  σ = √(5^2 ) = 5

Confidence Level = CL = 0.95

             Therefore, Confidence Interval = CI = µ ± Zα/2= 0.025(σ)

                                                                            = 540 ± 1.96(225)

                                                                             = (99,981) In Millions

Specify the 5th percentile of profit (in Rupees) for the company

         Ans :- Specify the 5th percentile of profit (in Rupees) for the company

          To calculate 5th percentile from Z table Zα/2= 0.05 = -1.645

                         5th percentile   = µ - Zα/2= 0.05(σ)

                                                    = 540 – 1.645(225)

                                                    = 169.87 Million