Question

Discrete:

Binomial - See Section 5.5 as to when you may use it.

Poisson - See Section 5.6 as to when you may use it.

Hypergeometric - See Section 5.7 as to when you may use it.

Continuous:

Uniform - See Section 6.1 as to when you may use it.

Normal - See Section 6.2

Exponential - See Section 6.4 as to when you may use it.

Your task for this discussion is as follows: As a manager of an organization, what probability distribution from this week would you use if you wanted to estimate your annual employee turnover? Explain why you would use it. Identify the statistical formulas specifically and what additional data you would need to determine your estimate(s).

Explain why your probability distribution applies.

Answer 1

Poisson Distribution:

* To estimate an annual employee turnover,the best probability distribution would be the poisson ditribution probability.
With this probability we can estimate the amount of times an event occurred within specific interval/period.

* The Poisson Distribution is a tool used in probability theory statistics to predict the amount of variation from a known average rate of occurrence, within a given time frame.

* Poisson Distribution can be used as follows:

a. To determine how much variation there will likely be from that average number of occurrences.

b.To determine the probable maximum and minimum number of times the event will occur within the specified time frame.

* The Poisson Distribution formula, where the mean (average) number of events within a specified time frame is designated by μ. The probability formula is:

P(x; μ) = (e)^-u (μ^x) / x!

Where:

x = number of times and event occurs during the time period

e (Euler’s number = the base of natural logarithms) is approx. 2.72

x! = the factorial of x (for example, if x is 3 then x! = 3 x 2 x 1 = 6)

Example:

μ = 5,
x = 9,
e = 2.71828

Insert the values into the distribution formula: P(x; μ) = (e)^-μ (μ^x) / x!

= (2.71828)^-5 (5^9) / 9!

= (0.0067) (1953125) / (3262880)

= 0.036

3.6% is the probability

* Poisson Distribution Validation:

a.k is the number of times an event happens within a specified time period, and the possible values for k are simple numbers such as 0, 1, 2, 3, 4, 5, etc.

b.There must be some interval of time – even if just half a second – that separates occurrences of the event.

c.The probability of an event happening within a portion of the total time frame being examined is proportional to the length of that smaller portion of the time frame.

d.The number of trials is sufficiently greater than the number of times the event does actually occur.