intro to normal distribution

Upload: sumanta1234

Post on 02-Jun-2018

225 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/10/2019 Intro to Normal Distribution

    1/22

    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?

  • 8/10/2019 Intro to Normal Distribution

    2/22

  • 8/10/2019 Intro to Normal Distribution

    3/22

  • 8/10/2019 Intro to Normal Distribution

    4/22

  • 8/10/2019 Intro to Normal Distribution

    5/22

  • 8/10/2019 Intro to Normal Distribution

    6/22

  • 8/10/2019 Intro to Normal Distribution

    7/22

  • 8/10/2019 Intro to Normal Distribution

    8/22

  • 8/10/2019 Intro to Normal Distribution

    9/22

  • 8/10/2019 Intro to Normal Distribution

    10/22

  • 8/10/2019 Intro to Normal Distribution

    11/22

  • 8/10/2019 Intro to Normal Distribution

    12/22

  • 8/10/2019 Intro to Normal Distribution

    13/22

    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.

  • 8/10/2019 Intro to Normal Distribution

    14/22

    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

  • 8/10/2019 Intro to Normal Distribution

    15/22

    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

  • 8/10/2019 Intro to Normal Distribution

    16/22

    ??

    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()

  • 8/10/2019 Intro to Normal Distribution

    17/22

    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.

  • 8/10/2019 Intro to Normal Distribution

    18/22

    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

  • 8/10/2019 Intro to Normal Distribution

    19/22

    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?

  • 8/10/2019 Intro to Normal Distribution

    20/22

    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.

  • 8/10/2019 Intro to Normal Distribution

    21/22

    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%.

  • 8/10/2019 Intro to Normal Distribution

    22/22

    Area Under the Standard Normal Curve