Question

Many research studies have been conducted to examine how different organizations are on implementing knowledge management process. For example, studies have proved that larger firms have more resources to utilize, and so they have taken more efforts to implement knowledge management process. The Journal of Business Research (Aug. 2014) published a study* discussing the relationship between knowledge management process and organizational performance. The table below shows the percentage of different size of firms participated in the study. These firms have been classified in terms of number of employees working.

	Micro (12 employees)	Small (40 employees)	Medium (75 employees)	Large (150 employees)	Very large (300 employees
% of companies	26.05	19.32	14.28	11.76	28.57

1. Randomly select one of the participated company from this study. Let x be the number of employees working in the company. Write the probability distribution of this x.

2. What is the probability that the selected company employs more than 50 employees?

3. Find E(x) and σ. Interpret the result.

Answer 1

1)

X	P(X)
12	0.2605
40	0.1932
75	0.1428
150	0.1176
300	0.2857

2)

Probability that employee >50 =

75	0.1428
150	0.1176
300	0.2857

P(X.>50 ) = 0.1428 + 0.1176 +0.2857 = 0.5461

3)

X	P(X)	X*P(X)	X² * P(X)
12	0.2605	3.126	37.512
40	0.1932	7.728	309.120
75	0.1428	10.710	803.250
150	0.1176	17.640	2646.000
300	0.2857	85.710	25713.000

X*P(X)	X² * P(X)
124.914	29508.88

mean = E[X] = Σx*P(X) =            124.9140
          
E [ X² ] = ΣX² * P(X) =            29508.8820
          
variance = E[ X² ] - (E[ X ])² =            13905.3746
          
std dev = √(variance) =            117.9211

Please revert back in case of any doubt.

Please upvote. Thanks in advance.