Probability Distribution

By Author: mohanchen
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probability distribution has a bell-shaped curve. It is characterized
by its mean mu and standard deviation sigma. The mean describes the location of the curve, the standard deviation describes the shape (how peaked or flat it is). The mean, the median, and the mode are all equal in a normal distribution.

To describe the time it takes to complete a task, you use the exponential probability distribution, For example, you can describe the time between arrivals of vehicles in a drive-through or the time required to load a crate of goods. Product lifetimes also often follow an exponential probability distribution.

For example, if the average lifetime of a part in a machine is 15 years, you can find the probability that the part will last less than a certain number of years, more than a certain number of years, or between numbers of years.
The EXPONDIST function uses the following syntax:
=EXPONDIST (x, lambda, cumulative)
where lambda is the inverse of the mean and cumulative allows you to tell Excel whether you want the cumulative probability ...
... or the probability of exactly that value. For example, if you want to find the probability that a part with a mean lifetime of 12 years lasts less than 6 years, enter the function as follows:
=EXPONDIST(6,1/12,TRUE)
The function returns the value 0.3935.

CRITBINOM Function

The acceptance criterion function, CRITBINOM, is used for quality control of a production process. You use this function to find the maximum number of defective items that a person can find in a lot and still allow acceptance of the lot. Inspectors should accept the lot if they find this number or fewer defective items and reject the lot if they find more defective items.

To determine the acceptance criterion, you need to know the number of items in the lot, the probability of accepting each item, and the producer's allowable risk (alpha) for rejecting an acceptable lot.
The CRITBINOM function uses the following syntax:
=CRITBINOM (trials, probability_s, alpha)
where trials is the number of trials, probability's is the probability of a success on each trial,
and alpha is the criterion value. Probability's and alpha are both between 0 and 1.

GAMMADIST Function
If you know x and want to find the probability, you use the GAMMADIST function, which
has the following syntax:
=GAMMADIST(x, alpha, beta, cumulative)
For example, if x equals 25, alpha equals 8, beta equals 9, and cumulative is TRUE, you
use the following formula:
=GAMMADIST (25,8,9,TRUE)
The function returns the value 0.007774.