Six Sigma Probability and Statistical Distribution

What are the characteristics of normal distribution?

*A narrow bell curve indicates a higher confidence in the data *Changes to the mean shift the normal curve horizontally *The tail extend to infinity *The mean lies at the center of the distribution

Sequence the steps for calculating cumulating probability from z-values

*Determine the Z-scores *Calculate the probabilities associated with each *Subtract the lower value from the higher one

In which examples could binomial distribution be used?

*Finding the probability a prototype unit will meet specification *Estimating the number of people that respond to a survey *Determining the probability of getting a certain number of question correct in an exam *Modeling the number of failure in a trial

What are the characteristics of an F-distribution curve?

*In an F-density curve, the peak is near one *It plots the ratios of two independent chi-square variable *The curve is right-skewed

Continuous

*Temperature *Cost *Length

Which statistics could be successfully modeled using the Poisson distribution?

*The annual number of emergency room visits by persons with no health care coverage *The density of particles emitted by a radioactive source within a volume of air *The number of mutation on a particular chromosome

Which observation about normal distribution curves are correct?

*The distribution of data is symmetric around the mean *A shift to the left indicates a decreasing mean *The mean, median, and mode coincide *They're defining by the mean and the standard deviation

What are some examples of results that could be successfully modeling using the Poisson distrubution?

*The number of accidents that occur on a particular highway in a given month *The daily number of unanswered tech support requests at a call center *The number of theater patrons who arrive within 30 minutes of the beginning of the play

What are the properties of chi-square distribution?

*The variance is equal to two times the number of degrees of freedom *As the degrees of freedom increase, the chi-square curve approaches a normal distribution *The mean of the distribution is equal to the number of degrees of freedom

What are the characteristics of F-distribution curves?

*They take only positive values *They have two degrees of freedom *They're characterized by two parameters

How are chi-square distributions used?

*To test the goodness of fit of an observed distribution to at theoretical one *To use reasonable assumptions to prove or disprove a hypothesis *To make inference about a larger population *To investigate whether distributions differ from one another

When are Student's t-distributions used?

*When sample sizes are small but populations are normal *When samples are drawn from populations with a normal bell-shaped distribution *When the standard deviation may not be known and has to be estimated from the data

Discrete

*Yes/No *Occupation *Number of team members

Assuming a standard 52-card deck, what's the probability of dealing three eights in a row when the cards are NOT returned to the deck between each draw?

0.018%

Three boxes in a shipment of 10 contain car parts. The probability of finding the first box is 0.1, the second 0.7, and the third 0.2. What's the probability of finding either the first or third box?

0.3

There are ten members in a Six Sigma team; four are Green Belts. If one team member is selected at random to work on a Kaizen project, what's the probability it will be one of the Green Belts?

0.4

A door alarm works 72 times out of 100, and video surveillance 68 times out of 100, to help a store catch thieves. If used together, what's the probability of the security techniques being effective?

0.49

You bring some treats to a meeting. The plate contains five donuts, three brownies, and two cookies. You select the treat nearest you. What's the probability you'll get either a brownie or a cookie?

0.5

A Six Sigma team has 20 members. Three are Black Belts. If two team members visit your desk, what's the probability that both visitors will be Black Belts and that the same person won't visit twice?

1.6%

Your Six Sigma team has ten members. You need three of them to be on a customer service committee. How many possible combination are there?

120

An electronics firm has twelve customer service representatives. A nine-member customer service team needs to be created. How many possible team combinations are there?

220

How many different ways can four team members from a group of fifteen be lined up for a photograph?

32760

A storage room contains five laptops, one of which is broken. What's the probability of randomly selecting the broken laptop on your visit to the room, and then selecting the same laptop the next day?

4%

Three different roles on a Six Sigma team need to be assigned. Nine team member with the specific skill set and experience are considered for the three positions. What's the premutation?

504

An outcome or collection of outcomes that are subsets of the sample space

Event

The measure of the likelihood of an event

Probability

The set of all possible outcomes

Sample space