There are two investment companies and each annual profit of both of them is nor

Question

There are two investment companies and each annual profit of both of them is normally distributed with the same positive mean. The standard deviation of company A’s annual profit is one half of its mean. In a given year, the probability that company B has a loss is 0.9 times the probability that company A has a loss. Now please show the ratio of the standard deviation of company B’s annual profit to the standard deviation of company A’s annual profit. There are two investment companies and each annual profit of both of them is normally distributed with the same positive mean. The standard deviation of company A’s annual profit is one half of its mean. In a given year, the probability that company B has a loss is 0.9 times the probability that company A has a loss. Now please show the ratio of the standard deviation of company B’s annual profit to the standard deviation of company A’s annual profit.

Explanation / Answer

Here let say mean of company A is a and standard deviation = a

given that,

a = a /2

Company A will have loss that means, if annual profit of a given year is X .then, X would be less than zero.

Pr(X < 0 ) = NORM(X <0 ;a  ; a /2)

Z = (0 - a) /(a /2 ) = -2

so, Pr(X < 0) = Pr(Z < -2)

by Z - table

Pr(X < 0) = Pr(Z < -2) = 0.02275

so now it is given that  company B has a loss is 0.9 times the probability that company A has a loss.

so If we say that company B will have loss when  if annual profit for company B of a given year is Y.then, Y would be less than zero.

Pr(Y < 0) = 0.9 * Pr(X < 0) = 0.9 * 0.02275 = 0.020475

so If mean profit of company B is b and standard deviation = b

so Pr(Y <0) = NORM(Y < 0 ; b ; b ) = 0.020475

so respective Z - value for the given p - value

Z -1 (0.020475) = -2.044

Z = 2.044 = b / b

so  b = b / 2.044

here a = b

so, b  = 2 a /2.044

b / a = 2/ 2.044

b / a = 1/1.022

b : a = 1 : 1.022

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---