Business Statistics

226 Business Statistics

Standard deviation of a uniform distribution =

150 120 30

8.6602

12 12 12

b a− −

σ = = = =

Figure 7.2 exhibits the solution of the train example with its mean and standard deviation.

7.2.2 Calculation of Probabilities in Uniform Probability Distribution

We have already discussed that the area under the curve, that is, area between a and b is equal to 1.

The probability of x £ a and x  b is zero because there is no area below a and beyond b. In a uniform

distribution, probabilities can be calculated as below:

2 1

( )

x x

P x

b a

−



=



−



where

1 2

a x x b≤ ≤ ≤

.

For the train arrival time example, we can calculate the probability of ...