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Business & Marketing
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Case Study
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Case Study: Expected New Members. Business & Marketing

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Case Study:
Leaders of a local club want to focus on recruiting and looked through their recruiting and membership paperwork. They realized that over the past 30 years of annual open-house events, they spoke to four people who were interested enough in joining to take an application packet home. The historical probability P(X) that the interested prospective members would join is below.
• 0 join: 0.1 
• 1 join: 0.2 
• 2 join: 0.4 
• 3 join: 0.2 
• 4 join: 0.1
When they hold an open house this year, how many members (what is the expected value) should they anticipate joining? 
Explain your approach to determining the number of expected new members in a three-page response. Be sure to research sources to support your ideas, and integrate your sources using APA-formatted citations and matching reference lists. Additionally, use Times New Roman 12pt. double-spaced font. 
Course Textbook(s)
Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2015). Quantitative analysis for management (12th ed.). Upper Saddle River, NJ: Pearson.

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Case Study: Expected New Members
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To determine the expected value of a variable, the sum of the products of the possible values ​​of the variables or random event multiplied by their respective probabilities. In the theory of probability and discrete distributions, the expected value represents the average value of a data set. This implies that to calculate the expected value of a variable, it is necessary to first determine the probability distribution. At the same time, to summarize the behavior of a random variable, the measure of central tendency of the random variable, the expected value of the random variable is used. Calculating the expected value and variance of a random variable given its distribution of probabilities helps in decision making and the expected value is the weighted average of the values.
Using the probability of each event the expected value is determined as
Probability P(X)
* 0 join: 0.1
* 1 join: 0.2
* 2 join: 0.4
* 3 join: 0.2
* 4 join: 0.1
Where x is the value of the event, P the probability of occurrence, and the period in which said event occurs and n is the total number of periods or observations (Render, Stair, Hanna & Hale, 2015). The outcomes are independent of each other, and the sum of the probabilities is 1, where the probabilities are also the relative frequencies. The probabilities used in the expected value calculation are based on past information where it is more likely that there will be similar behavior of the outcomes. The expected value E(X) with the summation of the product of the outcomes and probabilities that is then weighed is represented below
E(X) = (0 *0.1) + (1*0.2) + (2*0.4) + (3*0.2) + (4*0.1) =2
The rationale for using the expected value approach is that the weighted average is used unlike the case where the un-weighted average is used without considering the probability of each of the outcomes is weighed equally. Since the expected value is the sum of the number of members joining by their probability of happening. ...
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