Question

An investment portfolio contains stocks of a large number of corporations. Over the last year the rates of return on these corporate stocks followed a normal distribution with mean 9.5% and standard deviation 4.5%. (a)For what proportion of these corporations was the rate of return higher than 16%? (b)For what proportion of these corporations was the rate of return negative? (c)For what proportion of these corporations was the rate of return between 3% and 17%?

Answer 1

Answer:

In a normal distribution:

Formula for z value = z = (x – μ) / σ

1) X= 16%

μ= 9.5%

σ= 4.5%

z= 16-9.5/4.5

=1.555 (Look up this score on t he z table)

Probability = 0.9394 (this is the probability of the return being in between 0%-16%, if we want to find the probability of the return being lower than or equal to 16% we have to subtract  0.9394 from 1)

1-0.9394=0.0606=6.06% of the stocks had higher than 16% return.

2) 1) X= 0%

μ= 9.5%

σ= 4.5%

Z= 0-9.5/4.5=-2.11

Probability = 0.0174 = 1.74% of the stocks had a return below 0

3) 3<X>17

μ= 9.5%

σ= 4.5%

Z=3-9.5/4.5=-1.44= 0.0749

z= 17-9.5/4.5= 1.66=0.9515

We have the probability of the stocks that return below 3% (0.0749)

and stocks which return under 17% (0.9515)

In order to find the proportion of stocks between 3% and 17% we will subtract 0.0749 from 0.9515

=0.8766

For 87.66 % of these corporations the rate of return was between 3% and 17

Explanation: