intro to normal distribution
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A NOTE ON NORMAL DISTRIBUTION
As you might have learnt from prior courses in SCM, consumer demand is usually
unpredictable. Thus, we need a way to represent this unpredictable (or random)
demand in order to meaningfully study SCM. A normal distribution is the most
common representation of this random consumer demand. This note reviews some
preliminary info on the normal distribution. Please review this information
carefully before the assigned class. You can skip this reading if you are already
familiar with the normal distribution.
Here are some specific steps you might want to follow to facilitate your
learning.
1. Read this note carefully; discuss it with your friends. Is there anything that is
still unclear? Save the questions for the instructor and ask in the class.
2. Open Microsoft Excel and research the four functions: NORMDIST,
NORMSDIST, NORMINV, NORMSINV. Review the information providedin the help section of Excel about these four functions. What do these
functions compute?
3. There are three examples (one solved, two unsolved) towards the end of the
note. Solve them using both z-table and Excel.
4. There are two so-called z-tables in this note: one on p. 235 and the other on
the very last page. What is the difference between the two?
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Example 1
The manager would like to know the
chance (probability) of a stockout.
Pep Zone sells auto parts and supplies
including a popular multi-grade motor oil.
When the stock of this oil drops to20 gallons, a replenishment order is placed.
The store manager is concerned that
sales are being lost due to stockouts
while waiting for replenishment.
It has been determined that lead-timedemand is normally distributed with a
mean of 15 gallons and an SD
of 6 gallons.
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How do we find it?
2011: Excel
Ok probability or chance..
I get it, BUT
1980s: z-table
Convert X (or D, the demand) to z
Look at z-score or probability
NORMDIST function, or
NORMSDIST function
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x
Normal Distribution
in EXCEL - 1
Area Under Normal
Curve
NORMDIST(x 1)NORMSDIST([x )
Given: quantity or demand (x or z value)
Find: in-stock probabil ity (z-score) orstockout probability
Given: x
Find the shaded ar
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??
Normal Distribution
in EXCEL - 2
Given: probability (x or z score)
Find: Quantity (x or z value). X = +z
Given: shaded area
Find the ?? value (Qty)
From Area to X or z
NORMINV()
NORMSINV()
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Back to Example 1
The manager would like to know the
chance (probability) of a stockout.
Pep Zone sells auto parts and supplies
including a popular multi-grade motor oil.
When the stock of this oil drops to20 gallons, a replenishment order is placed.
The store manager is concerned that
sales are being lost due to stockouts
while waiting for replenishment.
It has been determined that lead-timedemand is normally distributed with a
mean of 15 gallons and an SD
of 6 gallons.
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Example 1: Pep Zone
z = (x - )/
= (20 - 15)/6 = .83
EXCEL:
NORMSDIST(0.83) =
0.7969
This is Pr{Z < 0.83}
Therefore,
Pr.{Z > 0.83} = Pr.{X > 20}
= 1- 0.7967 = 0.2033
z-Table:
Find z = 0.83, pick
corresponding prob:
F(0.83) = 0.7967
This is Pr{Z < 0.83}
x
Area
= .7967
Area = 1 - 0.7967
= 0.2033
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Example 2
You are the manager of the local Best Buy store.
Your weekly demand for Apple iPad follows a
normal distribution with mean 50 and SD 30. You
have 69 iPads in stock at the beginning of the week.
NoAdditional receipts are expected during the week.
What is the chance of stock-out during the week?
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In-stock Probability,Cycle Service Level,
Service Level
Chance of not having a stock-out during
any specified time period.
Definition
Place
order
Order
arrives
Place
order
Lead-time (L)
Stock-out probability = 1 CSL
= 1- in-stock prob.
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Example 3
(Opposite of Example 2)
You are the manager of the local Best Buy store.
Your weekly demand for Apple iPad follows a
normal distribution with mean 50 and SD 30. Howmany iPads should you stock to achieve a service
level of 95%.
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Area Under the Standard Normal Curve
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