Question

Question 4      

Stock’s Blue annual profit follows a Normal distribution, with mean £53 and standard deviation £9. Stock’s Red annual profit follows a Normal distribution, with mean £62 and standard deviation £6.

1. What is the probability that at a random year stock Blue will outperform stock Red?
2. Your portfolio consists of 2 Blue stocks and 3 Red stocks. What is the probability that your profit will exceed £330?

Answer 1

We are given the 2 distributions here as:

From the above 2 distribution, we get the distribution for the difference in 2 variables here as:

a) The probability that at a random year stock Blue will outperform stock Red is computed here as:

P( B > R)

P(B - R > 0)

Now from the above distribution, we convert this to a standard normal variable as:

Getting it from the standard normal tables, we get here:

Therefore 0.2028 is the required probability here.

b) The portfolio here is given as:

P = 2B + 3R

Therefore the distribution of P here is given as:

The required probability here is now computed as:

P(P > 330)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0677 is the required probability here.