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Measure – Probability. Specific review/prerequisite knowledge for this assignment includes arithmetic and statistics related to probability and distributions. In 1-2 page each, research and prepare the following.

Think of them as essays or mini-reports.

a. Define the following and give an example of where they are used in quality.

• Distribution

• Parameter vs statistic

• Variable vs value

• Population vs sample

b. Summarize the following distributions. Describe the types of data that fit the distributions and how the distributions are used in SS or

quality in general.

• Normal

• t

• Binomial

• Poisson

• Chi-square

• F

• Hypergeometric (not in book)

c. Study all pages in the Distribution Excel file. Also look at the probability spreadsheet. Try to get an understanding of patterns.

Considering Assignment VI and the previous parts of this assignment, study when, where, etc. the distributions could be used. Compare the spreadsheet values to values in tables (in the text book and elsewhere).

Answer the following using the Distribution Excel file, tables, by-hand and/or calculator work, or use other software or create your own spreadsheet. Describe the method you used to find the answers.

• If as a long-run average I am willing to accept 1% bad apples, what is the chance that in a basket of 100 apples I will get exactly 1 bad apple? Hints: long-run average indicates an infinite population situation, therefore use the binomial distribution. 1% = .01.

• Your average rate of customer complaints is 10 per day. You want to be able to handle at least 99% of the complaints the day they are made.

How many complaints should you be able to handle in one day? Hints: as a minimum, you want to be able to handle your normal load—which is not exactly 10 due to sampling error but an average of 10, some days will be more and some less. You want to be able to handle 99% of the complaints that are likely to happen. Because you are dealing with a steady rate, the Poisson would be a good distribution to use. The unknown is how many complaints to handle. This x or n amount of complaints would be the number that results in a cumulative probability of at least 99%.

• Your average rate of customer complaints is 10 per day. What is the probability you will go all day without a complaint?

• You have a lot of 1,000 parts. 5 are blue (or bad, or tasty, etc., any characteristic or event). If you sample 10 parts what is the probability of getting exactly 1 blue part, 1 or fewer, and more than 1?

• The part diameters are normally distributed. The lower tolerance limit corresponds to -2 z (minus two standard deviations below the mean). The upper tolerance limit corresponds to 3 z. What percent of parts will be out of tolerance?

• For +/- 4.5 sigma, will a sample size of 5 be big enough to allow you to have a 1% producer’s risk? Explain your reasoning. Hints: This requires some knowledge of statistics and quality terms and concepts. Because we have a sample and have stipulated a sigma (a standard deviation) we probably can assume a t distribution. A producer’s risk corresponds to the area in the tails.

d. Graduate students only: In addition to and similar to the above, solve a real-life industrial problem using one of the distributions. Include in the write up the background, problem, the results and enough detail so that the reader can determine if the distribution fit the data.

**Title:**
Statistics And Probability

**Length:**
4 pages
(1204 Words)

**Style:**
APA

**Preview**

**PROBABILITY DISTRIBUTION**

In statistics and probability, a pdf or a probability distribution function is a function that assigns a probability value to each subset of all possible outcomes that is that is measurable from a random procedure or a survey of a statistical inference. Examples of distributions are well observed in experiments whose sample spaces are none numerical resulting to a categorical distribution, experiments with sample spaces enclosed by random variables that are discrete resulting to a probability mass function and in experiments where sample spaces are encoded by random variables that are continuous resulting in a distribution that can be easily specified by a probability density function

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