to understand the way profit can deviate from the expected value. In the Bell Company case, the
variance is used. Briefly, the variance is a measure of how the random values set are distributed
from the mean value. When the variance is high, it implies that the mean of random values
spreads away or far from the mean. Hence a low variation is desirable. The random variable
variance is the expected of the standard deviation squared from the mean.
The variance is of the discrete variable is computed mathematically as follows:
Variance = E[(X-µ)2] = ∑[P(X)* (X-µ)2]
The respective medium and large scale expansion are as follows:
Medium-scale: 2,725
Large scale expansion: 12, 400
Therefore, the variation of profit relating to large scale expansion is higher compared to
the profit variation associated with the medium scale expansion.
The standard deviation then comes out as the measure of the risk. In this case, the
standard deviation is used to quantify the amount of variation of a set of data values of the Bell
company. Then standard deviation assumes the values of the square root of variance. When the
standard deviation is low, it symbolizes that the random values lean towards the expected value.
Hence, the lowered standard deviation shows the company has lower risk, and when it is high,
the deviation shows high risk.
The standard deviation of medium and large scale expansion is

CASE STUDY ANALYSIS
4
Medium: 52.20
Large: 11.355
The medium-scale expansion’s lower standard deviation illustrates that the project is less
risky than the large scale expansion project option. Hence, in minimizing the risk or uncertainty,
the medium-scale expansion is preferred.
Recommendation
Therefore, it is recommended that a medium-scale expansion project is an option for Bell
Company as it has high expected values and lower risk. Thus, management should choose
medium-scale expansion projects.

CASE STUDY ANALYSIS
5
References
Black, K. (2017).
Business statistics: For contemporary decision making
. Hoboken NJ: John
Wiley & Sons.

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- Fall '19
- Standard Deviation, Probability theory, Cauchy distribution