Question

1. The demand for a product of Carolina Industries varies greatly from month to month. Based on the past two years of data, the following shows the monthly demand at Carolina Industries.

    Unit Demand               # Months

300                              4

400                              6

500                              9

600                              5

1. If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product?
2. What are the variance and the standard deviation for the number of units demanded?

Answer 1

A random variable whose value can be counted is termed as discrete random variable . The tabular description of all the value that a discrete random variable can take along with the associated probability is termed as the case of discrete probability distribution  

Answer:-  

Let the variable X denote the unit demand for the product of California industries.

Unit demand(X)	Number of months	f(x)	x^2 .f(x)
300	4	=4/24=0.17	15300
400	6	=6/24=0.25	40000
500	9	=9/25=0.37	92500
600	5	=5/24=0.21	75600

Total no. Of month =24

=f(x) =1

= = 223400

(a) the expected value of the monthly demand can be computed as:

E(x) = =(300×0.17)+(400×0.25)+(500×0.37)+(600×0.21) =462

Thus, the monthly order quantity is 462 .

(b) the variance is given by

Var(x) =

=223400-(462)^2

=223400 - 213444

=9956

Thus ,variance is 9956.

Standard deviation (s) is given as:-

S=

=

=99.78

Thus, standard deviation is 99.78