Question

The basic materials stock sector, comprised of companies specializing in industrial commodities, had a very poor showing during the first six months of 2000. The average stock price in this sector was down an average of 27% for this period. Assume that the returns were distributed as a normal random variable with a mean of -27% and a standard deviation of 15%.

1. [3] If an individual stock were selected from this population, what is the probability that it would have a return of between -37 and -17%?

2. [3] If an individual stock were selected from this population, what is the probability that it would have made a profit – i.e. a return greater than 0.0%?

3. [3] If random samples, of 10 stocks were selected from this population. What proportion of the samples would have a mean return of between -37% and -17%?

4. [3] If random sample of 10 stocks were selected from this population, what proportion of the samples would have made a profit?

Answer 1

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The normal distribution parameters are given as:

Mean, Mu = -27%
Stdev, Sigma = 15%
n = 10

a.

P(-37<X<=-17)
Standardizing using the above formula:
= P( (-37-(-27)) /15 < Z< (-17-(-27)) /15
= P(-0.6668 < Z < .6668)
= 0.7475 - 0.2525
= 0.4950 ( round to 4 decimal places)

b.

P(X>0)
Standardizing using the above formula:
= P( Z > (0-(-27)) /15)
= P(Z> 27/15)
= P(Z>1.8)
= 1- P(Z<=1.8)
= 1 - 0.9641
= 0.0359 ( round to 4 decimal places)

c.

P(-37<Xbar<-17)
Standardizing using the above formula:
= P( (-37-(-27)) /(15/sqrt(10)) < Z< (-17-(-27)) /(15/sqrt(10))
= P(-2.1083 < Z < 2.1083)
= 0.9825 - 0.0175
= 0.9650 ( round to 4 decimal places)

d.

P(Xbar> 0)
= P(Z> (0-(-27))/ (15/sqrt(10))
= P(Z>5.6921)
= 1-P(Z<=5.6921)
= 6.27432*10^-09
= 0.0000 ( round to 4 decimal places)