Deliverable 07 Worksheet Part 1 The First Item You Wa 386102

Deliverable 07 Worksheetpart 1the First Item You Want To Highlight I

Deliverable 07 – Worksheet Part 1 The first item you want to highlight is your customer satisfaction record. Over the past 18 months of employment, you worked with 25 clients, and according to customer satisfaction surveys, 22 of them rated you with the highest level of satisfaction. Use this information to find the best predicted probability of having a new client give the highest level of satisfaction. G & B Consulting prioritizes maintaining high ethical standards and receiving the highest rating from the Better Business Bureau consistently. To sustain this rating, at least 85% of customers must give you high satisfaction ratings. Internal projections predict serving 60 clients over the next year. As project manager, using your prior record as an indicator, find the probability that 85% or more of new clients will give the highest satisfaction rating. Show all calculations and formulas used, including Excel if applicable.

Use this information to make a convincing argument that you are a good choice for the position. Structure the paper with the following: You will first calculate the probability of getting a satisfied client based on your prior work history; then, explain how you found this solution. Next, calculate the probability that at least 85% of clients will give high satisfaction ratings and explain that process. Finally, interpret these results and argue why you are suitable for the position.

Paper For Above instruction

Understanding and analyzing customer satisfaction metrics are essential components of effective management and operational success within consulting firms like G & B Consulting. The ability to predict the likelihood that future clients will rate services highly hinges on prior satisfaction data, which, in this case, demonstrates a strong track record. By leveraging this historical data, we can utilize probability theory to assess the prospective success rate and compliance with the company’s standards for maintaining the Better Business Bureau (BBB) accreditation.

Calculating the Probability of a High Satisfaction Client

The primary data point involves 25 clients served over the past 18 months, with 22 of them rating service as the highest satisfaction level. This provides a sample proportion (p̂) of satisfied clients:

p̂ = 22/25 = 0.88

This proportion indicates that, based on historical data, each new client has an approximately 88% chance of providing the highest satisfaction rating. To determine this estimate's robustness, we can model it using a binomial distribution, under the assumption that each client’s satisfaction is independent and identically distributed (Lehmann & Romano, 2005). Alternatively, for large expected sample sizes, a normal approximation can be applied to estimate the confidence interval around this probability.

Using the normal approximation, the standard error (SE) for p̂ is:

SE = √[p̂(1 - p̂) / n] = √[0.88 × 0.12 / 25] ≈ 0.0649

A 95% confidence interval for the true proportion p is:

p̂ ± 1.96 × SE = 0.88 ± 1.96 × 0.0649 ≈ (0.752, 1.008)

Since the upper limit cannot exceed 1, we interpret this as approximately 75.2% to 100.0%. This interval affirms that, with high confidence, the true satisfaction rate is likely above 75%, and given the point estimate of 88%, it strongly suggests a high likelihood of future satisfaction from new clients.

Assessing the Probability of Maintaining an 85% Satisfaction Rate

The next step is to evaluate whether the company can expect at least 85% of clients to rate satisfaction highly, based on prior data. Assuming 60 clients will be served over the next year, we model the number of satisfied clients (X) as a binomial random variable:

X ~ Binomial(n=60, p=0.88)

We are interested in the probability that at least 85% of these clients, i.e., 0.85 × 60 = 51 clients, give high ratings:

P(X ≥ 51)

Using the normal approximation to the binomial distribution:

- Mean (μ):

μ = n × p = 60 × 0.88 = 52.8

- Standard deviation (σ):

σ = √[n × p × (1-p)] = √[60 × 0.88 × 0.12] ≈ 2.94

Applying a continuity correction:

P(X ≥ 51) ≈ P(Y ≥ 50.5),

Y ~ N(μ=52.8, σ=2.94)

Calculating the z-score:

z = (50.5 - 52.8) / 2.94 ≈ -0.77

Consulting standard normal distribution tables:

P(Z ≥ -0.77) ≈ 0.7794

Hence, there is approximately a 77.94% chance that at least 85% of the clients will be highly satisfied, given the historical satisfaction rate.

Interpreting the Results and Making an Argument for the Position

The statistical analysis indicates a strong likelihood that future clients will rate the services at a satisfactions level of 85% or higher. With an estimated probability of around 78% that at least 51 out of 60 clients (which equates to roughly 85%) will rate the service highest, I convincingly demonstrate my capability to maintain high client satisfaction standards (Agresti & Coull, 1998). The high satisfaction rate shows consistent quality of service, aligning with G & B Consulting’s objective of preserving an excellent BBB rating.

Furthermore, these probabilities reflect positively on my management and client interaction skills, emphasizing my proficiency in client relationship management. This quantitative evidence underlines my suitability for the project manager role, where ensuring high customer satisfaction is paramount. The calculated confidence intervals and probabilities offer a statistically supported argument that I am capable of delivering the high satisfaction levels required for continued top-tier BBB accreditation, reinforcing my candidacy convincingly.

References

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• Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses (3rd ed.). Springer.
• Newcombe, R. G. (1998). Two-sided confidence intervals for the binomial probability p. The American Statistician, 52(2), 127–131.
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