This ppt on Normal Distribution is useful in Finding the Probability using normal curve which is useful in calculating probability.

1. Normal
Distribution –Finding
Probability
SUNDARA B. N.
Assistant
Professor

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. 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. 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. 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. 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