Question

a venture capitalist feels that the annual rate of return on a proposed investment has a mean of 0.30 per share and standard deviation of 0.10 per share.

a) find the probability that the return will be less than 0.23 per share. Assume the returns are normally distributed.

b) find the probability that the return will be between 0.23 and 0.35 per share assume all returns are normally distributed

Answer 1

a)

µ = 0.3    

σ = 0.1

left tailed

X ≤ 0.23

  

Z =(X - µ ) / σ =-0.70

  

P(X ≤0.23) = P(Z ≤-0.70) =0.2420(answer)

b)

µ = 0.3        

σ = 0.1

we need to calculate probability for ,

0.23≤ X ≤ 0.35

X1 = 0.23,X2 =0.4

  

Z1 =(X1 - µ ) / σ =-0.700

Z2 =(X2 - µ ) / σ =0.500

  

P (0.23 < X < 0.35) = P ( -0.7< Z < 0.500)

  

= P ( Z < 0.500) - P ( Z <-0.700) = 0.6915 - 0.2420 = 0.4495(answer)

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excel formula for probability from z score    =normsdist(z)