Question

5. 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

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

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

Which of the two divisions has a larger probability of making a loss in a given year?

Explanation:

import numpy as np

from scipy import stats

from scipy.stats import norm

Mean = 5+7

print('Mean Profit is Rs', Mean*45,'Million')

SD = np.sqrt((9)+(16))

print('Standard Deviation is Rs', SD*45, 'Million')

print('Range is Rs',(stats.norm.interval(0.95,540,225)),'in Millions')

X= 540+(-1.645)*(225)

print('5th percentile of profit (in Million Rupees) is',np.round(X,))

print('Range is Rs',(stats.norm.interval(0.95,540,225)),'in Millions')

X= 540+(-1.645)*(225)

print('5th percentile of profit (in Million Rupees) is',np.round(X,))

stats.norm.cdf(0,5,3)

stats.norm.cdf(0,7,4)