This Assignment Is To Apply The Quality Tools For Solving Pr

This assignment is to apply the quality tools for solving problems, 6

This assignment is to apply the quality tools for solving problems, 6 problems with a total of 40 points. You’ll show the details of your calculation, draw a diagram, and answer questions. If you draw the diagrams by hand you can scan and attach as a file.

1. Using the following sample data below and attachment for reference, calculate the mean, mode, median, minimum, maximum, standard deviation, and range:

1.116, 1.116, 1.133, 1.117, 1.119, 1.119, 1.121, 1.128, 1.122, 1.125, 1.121, 1.136, 1.125, 1.124, 1.122, 1.125, 1.118, 1.123, 1.122, 1.122, 1.119.

Note: Excel Spreadsheet also has a function for finding these values; mean (average), mode, median, min, max, standard deviation (stdev), and range. Top menu, click “Formulas”, then “Insert Function” (on your far left), then you will see a box. Select a category, “Statistical”, from a drop-down menu.

2. If the average wait time is 12 minutes with a standard deviation of 3 minutes, determine the percentage of patrons who wait less than 15 minutes for their main course to be brought to their tables.

Paper For Above instruction

Applying quantitative quality tools and statistical analysis plays a crucial role in enhancing decision-making processes and improving operational efficiency. This paper addresses two primary objectives: first, to perform descriptive statistical calculations on a provided data set; second, to analyze a probability scenario involving customer wait times to determine service performance levels. Each task demonstrates the application of fundamental statistical tools such as mean, median, mode, standard deviation, and range, alongside probability assessments based on the normal distribution assumption.

Starting with the descriptive statistics, the provided data set consists of 21 observations of a measurement, with the goal of summarizing its central tendency, dispersion, and distribution characteristics. Calculating the mean involves summing all values and dividing by the number of observations, which yields an average of approximately 1.123. The mode, representing the most frequently occurring value, is 1.122, since this value appears most often in the data set. The median, the middle value when data points are ordered from smallest to largest, is approximately 1.122, indicating the center point of the data distribution. The minimum value is 1.116, and the maximum value is 1.136, providing insights into the data's range of variation.

The range, computed as the difference between the maximum and minimum, is approximately 0.020, reflecting the spread of data points. Standard deviation, a measure of data variability, is calculated to be approximately 0.007, indicating that most data points are closely clustered around the mean. These statistical measures collectively depict a distribution with moderate central tendency and tight dispersion, characteristic of consistent measurement data.

Transitioning to the probability problem, the customer wait time is modeled assuming a normal distribution with a mean of 12 minutes and a standard deviation of 3 minutes. To determine the percentage of patrons waiting less than 15 minutes, the standard normal distribution (Z-distribution) is employed. The Z-score corresponding to 15 minutes is calculated: Z = (X - μ)/σ = (15 - 12)/3 = 1.0. Consulting standard normal distribution tables or using statistical software reveals that approximately 84.13% of the population waits less than 15 minutes.

This analysis indicates that a significant majority of patrons experience timely service, with over 84% waiting less than 15 minutes. Such insights are valuable for evaluating service quality, identifying improvement opportunities, and setting realistic performance benchmarks. Moreover, graphical representations such as histograms or normal distribution curves can aid in visualizing data characteristics and probability assessments, facilitating communication and decision-making.

In conclusion, applying statistical tools to both data analysis and probability modeling is essential for quality management and operational excellence. Descriptive statistics provide a clear snapshot of data behavior, while probability calculations enable service providers to understand and improve customer experiences. Together, these tools foster data-driven decision-making, continuous improvement, and enhanced customer satisfaction in various operational contexts.

References

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• Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability & Statistics for Engineering and the Sciences. Pearson.
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