Answer to Question #215484 in Statistics and Probability for Sagar Sah

Question

A project yields an average cash-flow of Rs. 400 lakh with a standard deviation of Rs. 60 lakh. Calculate the following probabilities: (i) Cash flow will be more than Rs. 550 lakh (ii) Cash flow will be between Rs. 450 lakh and Rs. 520 lakh.

Answer 1

Let $X=$ cash flow: $X\sim N(\mu, \sigma^2).$

Given $\mu=400, \sigma=60.$

(i)

$$P(X>550)=1-P(X\leq 550)$$

$$=1-P(Z\leq \dfrac{550-400}{60})$$

$$=1-P(Z\leq 2.5)$$

$$\approx0.0062$$

(ii)

$$P(450<X<520)=P(X<520)-P(X\leq 450)$$

$$=P(Z< \dfrac{520-400}{60})-P(Z\leq \dfrac{450-400}{60})$$

$$=P(Z<2)-P(Z\leq 0.8333)$$

$$\approx0.97725-0.79767\approx0.1796$$