TAYLOR’S BUSINESS SCHOOL

TU/UWE Dual Awards Business Programmes

STA60104 Quantitative Methods for
Business

Formulae and Distribution Tables

Mathematical Formulae
1.

Simple Interest:

A=P(1+rt)

2.

Compound Interest: A=P(1+i)n

 1  i n  1
3. Future Value: FV=PMT 

i


1  (1  i )  n
4. Present Value: PV  PMT  i or

PMT= FV 

i
(1  i) n  1

or

PMT= PV 

i
1  (1  i ) n

Statistical Formulae

x

1.

Sample Mean: x 

2.

Sample Standard Deviation

n

n

s

3.

 (x i 1

i

 x)2

2

or

n 1

Coefficient of variation =

1 
 x 2   x 

n 1 n 

s






s
( )(100 )% x 4. Probability
(a) General Rule of Addition: P ( A  B )  P ( A)  P ( B )  P ( A  B )
(b) Special Rule of Addition: P ( A  B )  P ( A)  P ( B )
(c) Special Rule of Multiplication: P ( A  B )  P ( A) P ( B )
(d) Conditional probability rule:

P( A B)  P( AandB) / P( B)

(e) The conditional probability rule for independence testing:
5.

Discrete Probability Distribution
(a)

E ( X )   xP( x)

 x  E(X 2 )  [E(X)]2
(b) Binomial Distribution

P(X  x)n Cx  p x  (q) nx
Mean    np
2
Variance    npq
(c) Poisson Distribution

P(X  x ) 
6.

e   x x! Continuous Probability Distribution
(a) Standard Normal Value: z 

x



P( A B)  P( A)

(b) Mean of x to a z-score:

z

x

 n 7.

Confidence Interval for mean:
(a)
(b)





known: x  z



unknown: x  t

n s with df=n-1

n

8.

Confidence Interval for proportion ( ):

9.

p(1  p) n pz

Test Statistics:
(a) z-distribution as a test statistics

z

x

 n t

(b) One sample test of mean, small sample

x s n

 z 

 e 

2

10. Sample Size for Estimating Mean: n  

11.