2 A venture capital company feels that the rate of return X

2. A venture capital company feels that the rate of return (X) on a proposed investment is approximately normally distributed with mean 30% and standard deviation 10%. (a) Find the probability that the return will exceed 55%. (b) Find the probability that the return will be less than 25% (c) What is the expected value of the return? (d) Find the 75th percentile of returns.

Solution

(a) Find the probability that the return will exceed 55%.

P(X>55) = P((X-mean)/s >(55-30)/10)

=P(Z>2.5) = 0.0062 (from standard normal table)

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(b) Find the probability that the return will be less than 25%

P(X<25) = P(Z<(25-30)/10)

=P(Z<-0.5) = 0.3085 (from standard normal table)

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(c) What is the expected value of the return?

expected value= 30

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(d) Find the 75th percentile of returns.

P(X<c)=0.75

--> P(Z<(c-30)/10) =0.75

--> (c-30)/10 = 0.67 (from standard normal table)

So c=30+0.67*10=36.7