Question

An investment company A has an expected return of $2,000 with a standard deviation of $200. An investment in company B has an expected return of $3,000 with a standard deviation of $100. If the returns are normally distributed and independent, what is the probability that the total return from both investments will be at least $5,000?

Answer 1

SOLUTION:

From given data,

An investment company A has an expected return of $2,000 with a standard deviation of $200. An investment in company B has an expected return of $3,000 with a standard deviation of $100. If the returns are normally distributed and independent, what is the probability that the total return from both investments will be at least $5,000

It is given information

It is given information that the expected returns of two companies.

Let X denotes the expected return of company A

It follows normal distribution with mean $2000 and a standard deviation of $200.

Let Y denotes the expected return of company B, It follows normal distribution with mean $3000 and a standard deviation of $100 .

E(X+Y )= E(X)+E(Y)

=$2000+$3000

= $5000

Var( X + Y)= Var(X)+ Var(Y)

= ($200)² + ($100)²

= $50000

SD(X+Y ) =
=

=

  

Now we need to find the probability that the return from both investments will be at least $ 5000

That is P(X+Y > 5000)

P(X+Y > 5000) = 1 - P [ (X+Y) - () / < 5000-5000 / ]

= 1 - P [ Z < 0 ]

= 1 - 0.5000

= 0.5

Therefore the probability that the return from both investments will be at least $5000 is 0.5