Question

Suppose that the annual return, R on a share is normally distributed with an expected annual return of 10% and an annual standard deviation of 20%.

Find using the Table of the normal distribution provided, the probability that the annual return on the share will:

(i) Be positive. [2]

(ii) Be less than -5%. [2]

(iii) Lie between 5% and 15%. [2]

(iv) Be within one standard deviation of zero. [2]

(v) Be within one standard deviation of its mean. [2]

Answer 1

[Used R-Software]

R-commands and outputs:

# X ~ N(mu,sigma) (X : annual return R)
mu=10/100
sigma=20/100

# (i) Be positive
# P(X > 0)
1-pnorm(0,mu,sigma)
[1] 0.6914625

# (ii) Be less than -5%.
# P(X < (-5/100))
pnorm((-5/100),mu,sigma)
[1] 0.2266274

# (iii) Lie between 5% and 15%
# P(0.05 < X < 0.15)=P(X<0.15)-P(X<0.05)
pnorm(0.15,mu,sigma)-pnorm(0.05,mu,sigma)
[1] 0.1974127

# (iv) Be within one standard deviation of zero
# This means P(0-sigma < X < 0+sigma)
pnorm(0+sigma, mu, sigma)-pnorm(0-sigma, mu, sigma)
[1] 0.6246553

# (v) Be within one standard deviation of its mean
# This means P(mu-sigma < X < mu+sigma)
pnorm(mu+sigma, mu, sigma)-pnorm(mu-sigma, mu, sigma)
[1] 0.6826895

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