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# Binomial Distribution Modeling: Defective Part Rate in Manufacturing

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A manufacturer has determined that on one of its assembly lines, the defective part rate is 60000 PPM (Parts Per Million), corresponding to a probability of producing a defective part of 6%. You are a Quality Engineer and told by the manufacturer's accountants that they can afford for you to take a sample of 20 parts every hour to aid in determining the actual number of defectives at that time, but they can afford no greater disruption to production. What is the minimum number of defective parts you need to find in the sample to support management's decision to shut down the line if, within a 95% confidence interval, your evidence suggests the tolerant 60000 PPM rate has been exceeded? The company uses Microsoft products as an office standard, so you are required to use Excel to present your reasoning.

#### Solution Summary

Excel's binomial function modeling a null hypothesis test in a completed spreadsheet is used to explore application of basic probability of this story problem and its implications.

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## Statistics Population Defective Parts

1. If 10% of a population of parts is defective, what is the probability of randomly selecting 80 parts and finding that 12 or more parts are defective?

2. A survey was taken of U.S. companies that do business with firms in India.
One of the questions on the survey was: Approximately how many years has your company been trading with firms in India? A random sample of 44 responses to this question yielded a mean of 10.455 years. Suppose the population standard deviation for this question is 7.7 years. Using this information, construct a 90% confidence interval for the mean number of years that a company has been trading in India for the population of U.S. companies trading with firms in India

3. A clothing company produces men jeans. The jeans are made and sold with either a regular cut or a boot cut. In an effort to estimate the proportion of their men jeans market in Oklahoma City that prefers boot-cut jeans, the analyst takes a random sample of 212 jeans sales from the company to Oklahoma City retail outlets. Only 34 of the sales were for boot-cut jeans. Construct a 90% confidence interval to estimate the proportion of the population in Oklahoma City who prefer boot-cut jeans.

4. In an attempt to determine why customer service is important to managers in the United Kingdom, researchers surveyed managing directors of manufacturing plants in Scotland.* One of the reasons proposed was that customer service is a means of retaining customers. On a scale from 1 to 5, with 1 being low and 5 being high, the survey respondents rated this reason more highly than any of the others, with a mean response of 4.30. Suppose U.S.
Researchers believe American manufacturing managers would not rate this reason as highly and conduct a hypothesis test to prove their theory. Alpha is set at .05. Data are gathered and the following results are obtained. Use these data and the eight steps of hypothesis testing to determine whether U.S. managers rate this reason significantly lower than the 4.30 mean ascertained in the United Kingdom. Assume from previous studies that the population standard
deviation is 0.574.
3 4 5 5 4 5 5 4 4 4 4 4 4 4 4 5 4 4 4 3 4 4 4 3 5 4 4 5 4 4 4 5 5

5. A study is conducted using only Boeing 737s traveling 500 miles on comparable routes during the same season of the year. Can the number of passengers predict the cost of flying such routes? It seems logical that more passengers result in more weight and more baggage, which could, in turn, result in increased fuel consumption and other costs. The data are the costs and associated number of passengers for twelve 500-mile commercial airline flights
using Boeing 737s during the same season of the year. Based on the results given below, answer
the following questions.
a) Check the conditions for a hypothesis test and CI of slope.
b) Test to see if there is a significant relationship between the 2 variables.
c) Construct and interpret a 95% CI for the slope.
d) Suppose a flight gets 75 passengers. What would their expected GPA be? Is this a good estimate? Explain in terms of R-sq

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