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### Normal Distribution - Find the Probability

1. 1. Normal Distribution –Finding Probability SUNDARA B. N. Assistant Professor
2. 2. Problem ABC ltd., is considering a project. The projected average cash out flow is Rs. 600 Lakh with a Standard Deviation Rs. 40 Lakh. Calculate a) The probability of cash flow being less than Rs. 660 Lakh b) The probability of cash flow being more than Rs. 500 Lakh c) The probability of cash flow being between Rs. 480 lakh and Rs. 560 lakh
3. 3. Given Information Here we are given that μ = Rs. 600 Lakh σ = Rs. 40 Lakh  X~N(600, 1600), We know that is X~N(μ, σ²), then the S.N.V is given by Z = X – μ σ
4. 4. i) The probability of cash flow being less than Rs. 660 Lakh Consider X = 660  P(X<660)=P(Z<1.5 ) = 0.5+P(0<Z<1.5) = 0.5+0.4332(TV) =0.9332 The probability of cash flow being less than Rs. 660 Lakh = 0.9332 Z=1.5 Z=0 X=600 X=660
5. 5. ii) The probability of cash flow being more than Rs. 500 Lakh Consider X = 500  P(X>500)=P(Z>-2.5) =P(Z>2.5) = 0.5+P(0<Z<2.5) = 0.5+0.4938 (TV) =0.9938 The probability of cash flow being more than Rs. 500 Lakh =0.9938 Z=0 Z=-2.5 X=600 X=500
6. 6. iii) The probability of cash flow being between Rs. 480 lakh and Rs. 560 lakh Consider X = 480 and X = 560  P(480<X<560)=P(-3<X<- 1) = P(-3<X<0)-P(0<Z<-1) = P(0<Z<3)-P(0<Z<1) = 0.4987-0.3413 (TV) =0.1574 The probability of cash flow being between Rs. 480 lakh and Rs. 560 lakh =0.1574 Z=0 Z=-1 Z=-3 X=480 X=600 X=560