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Suppose that your estimates of the possible one-year returns from investing in the common stock of the A. A. Eye-Eye Corporation were as follows:Probability of occurrence0.10.20.40.20.1Possible return10%5%20%35%50%a. What are the expected return and standard deviation?b. Assume that the parameters that you just determined [under Part (a)] pertain to a normal probability distribution. What is the probability that return will be zero or less? Less than 10 percent? More than 40 percent? (Assume a normal distribution.)
Given, Probability of occurrence Possible return 0.1 10% 0.2 5% 0.4 20% 0.2 35% 0.1 50% a Expected Value =0.1*-10%+0.2*5%+.4*20%+0.2*35%+0.1*50% 20.00% The standard deviation is calculated as below. Probability of occurrence Possible return X Expected Return E(X) Variance(X-E(X))^2 Probability*Variance 0.1 -10% 20% 0.09 0.009 0.2 5% 20% 0.0225 0.0045 0.4 20% 20% 0 0 0.2 35% 20% 0.0225 0.0045 0.1 50% 20% 0.09 0.009 Total Variance= 0.027 Standard Deviation = sq (variance) = 16.43% Therefore, the mean is 20% and the variance is 16.43% b. i. Probability that the return will be less than zero Use the normal distrubution table, p (X<0) (X-mean)/St dev = (0-.2)/.1643 = -1.22 Using the standard table P(Z<-1.22) = 0.1112 Therefore, the probability that the return will be less than 0 is... 0.1112 ii Probability that the return will be less than 10% Use the normal distrubution table, p (X<0.1) (X-mean)/St dev = (0.1-.2)/.1643 = -0.61 Use the standard table, P(Z<0.1)= 0.2709 Therefore, the probability that the return will be less than 10% is 0.2709 iii Probability that the return will be more than 40% Use the normal distrubution table, p (X>0.4) (X-mean)/St dev = (0.4-.2)/.1643 = 1.22 Use the standard table, P(Z>1.22)= 0.1112 Therefore, the probability that the return will be greater than 0.4 is 0.1112

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