Customer Service Department For Wholesale Electronics

The Customer Service Department For A Wholesale Electronics Outlet Cla

The customer service department for a wholesale electronics outlet claims that 90 percent of all customer complaints are resolved to the satisfaction of the customer. In order to test this claim, a random sample of 10 customers who have filed complaints is selected. 2.1 Let X be the number of sampled customers whose complaints were resolved to the customer’s satisfaction. What are the possible values (outcomes) of X?

Paper For Above instruction

The problem involves understanding the possible outcomes for a binomial random variable in the context of customer complaints resolution. Specifically, the company claims that 90% of customer complaints are resolved satisfactorily, and a sample of 10 complaints is examined to evaluate this claim. The variable of interest, X, represents the number of customers in the sample whose complaints were successfully resolved to their satisfaction. To determine the possible outcomes of X, it is essential to understand the nature of the variable and the structure of the sampling process.

Understanding the Context and Nature of X

X is a discrete random variable that counts the number of successful complaint resolutions among the 10 sampled customers. Since each customer’s complaint can either be resolved satisfactorily or not, X follows a binomial distribution, which is suitable for modeling the number of successes in a fixed number of independent Bernoulli trials with the same probability of success. The binomial distribution is characterized by two parameters: the number of trials (n) and the probability of success in each trial (p).

Parameters of the Binomial Distribution

In this case, the number of trials, n, is 10, representing the 10 sampled complaints. The probability of success, p, is 0.90, reflecting the company's claim that 90% of complaints are resolved satisfactorily. The binomial probability mass function (pmf) is given by:

P(X = k) = C(n, k) p^k (1 - p)^{n - k}

where C(n, k) denotes the binomial coefficient, calculating the number of ways to choose k successes out of n trials.

Possible Outcomes for X

Since X counts the number of successes (resolved complaints) among 10 customers, it can take any integer value from 0 to 10, inclusive. This is because it's possible, though perhaps unlikely, that none of the complaints in the sample were resolved satisfactorily (X=0), or that all were resolved (X=10). The possible outcomes are therefore all integers in this range:

  • X = 0
  • X = 1
  • X = 2
  • X = 3
  • X = 4
  • X = 5
  • X = 6
  • X = 7
  • X = 8
  • X = 9
  • X = 10

These outcomes comprehensively represent all possible counts of successfully resolved complaints within the sample of 10 customers.

Implications of the Outcomes

The range of outcomes allows for various analyses, such as calculating the probability of observing a specific number of successful resolutions or testing the company's claim by assessing whether the observed data significantly deviates from the claimed 90% success rate. For example, if the sampled data shows only 7 out of 10 complaints resolved satisfactorily, this corresponding value of X (i.e., 7) can be used to compute the probability under the binomial model, and infer whether the company's claim is consistent with the observed data.

Conclusion

The possible outcomes of the binomial variable X, which represents the number of customer complaints successfully resolved in a sample of 10, are all integers from 0 to 10 inclusive. This range reflects the inherent variability in the sampling process and forms the basis for statistical inference regarding the company's claim of a 90% success rate in resolving customer complaints.

References

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