7.2 - Minitab Express: Finding Proportions

7.2 - Minitab Express: Finding Proportions

Minitab Express can be used to find the proportion of a normal distribution in a given range. The default is to construct a standard normal distribution, but the mean and standard deviation of the distribution can be edited. The following pages will walk through how to construct normal distributions to find the proportion greater than a given value, the proportion less than a given value, or the proportion between two given values.


7.2.1 - Proportion 'Less Than'

7.2.1 - Proportion 'Less Than'

The cumulative probability for a value is the probability less than or equal to that value. In notation, this is \(P(X\leq x)\). The proportion at or below a given value is also known as a percentile.

MinitabExpress  – Proportion Less Than a z Value

Question: What proportion of the standard normal distribution is less than a z score of -2?

Recall that the standard normal distribution (i.e., distribution) has a mean of 0 and standard deviation of 1. This is the default normal distribution in Minitab Express.

Steps
  1. On a PC: from the menu select STATISTICS > Distribution Plot
    On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
  2. Select Display Probability (Note: The default is the standard normal distribution)
  3. Select A specified X value
  4. Select Left tail
  5. For X value enter -2

    This should result in the following output:

    Minitab Express output: z distribution showing the proportion less than -2

    The proportion of the z distribution that is less than -2 is 0.0227501.

    Video Walkthrough

    Select your operating system below to see a step-by-step guide for this example.

    MinitabExpress  – Proportion Less Than a Value on a Normal Distribution

    Scenario: Vehicle speeds at a highway location have a normal distribution with a mean of 65 mph and a standard deviation of 5 mph. What is the probability that a randomly selected vehicle will be going 73 mph or slower?

    Let's construct a normal distribution with a mean of 65 and standard deviation of 5 to find the area less than 73.

    Steps
    1. On a PC: from the menu select STATISTICS > Distribution Plot
      On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
    2. Select Display Probability 
    3. For Distribution select Normal (Note: This is the default)
    4. For Mean enter 65
    5. For Standard deviation enter 5
    6. Select A specified X value
    7. Select Left tail
    8. For X value enter 73

      This should result in the following output:

      Distribution Plot - Normal, Mean=65, StDev=5; Less Than

      On a normal distribution with a mean of 65 and standard deviation of 5, the proportion less than 73 is 0.945201 

      In other words, 94.5201% of vehicles will be going less than 73 mph.

      Video Walkthrough

      Select your operating system below to see a step-by-step guide for this example.


      7.2.1.1 - Video Example: P(Z<-1)

      7.2.1.1 - Video Example: P(Z<-1)

      Question: What proportion of the z distribution falls below a z score of -1?

      Steps
      1. On a PC: from the menu select STATISTICS > Distribution Plot

        On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot

      2. Select Display Probability (Note: The default is the standard normal distribution)
      3. Select A specified X value
      4. Select Left tail
      5. For X value enter -1
      Video Walkthrough

      This video is available in both Windows and Mac platforms. Select your platform below.


      7.2.1.2 - Video Example: P(SATM<540)

      7.2.1.2 - Video Example: P(SATM<540)

      Question: SAT-Math scores are normally distributed with a mean of 500 and standard deviation of 100. What proportion of scores are less than 540?

      Steps
      1. On a PC: from the menu select STATISTICS > Distribution Plot
        On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
      2. Select Display Probability 
      3. For Distribution select Normal (Note: This is the default)
      4. For Mean enter 500
      5. For Standard deviation enter 100
      6. Select A specified X value
      7. Select Left tail
      8. For X value enter 540

      Video Walkthrough


      7.2.2 - Proportion 'Greater Than'

      7.2.2 - Proportion 'Greater Than'

      MinitabExpress  – Proportion Greater Than a z Value

      Question: What proportion of the standard normal distribution is greater than a z score of 2?

      Recall that the standard normal distribution (i.e., distribution) has a mean of 0 and standard deviation of 1. This is the default normal distribution in Minitab Express.

      Steps
      1. On a PC: from the menu select STATISTICS > Distribution Plot
        On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
      2. Select Display Probability (Note: The default is the standard normal distribution)
      3. Select A specified X value
      4. Select Right tail
      5. For X value enter 2

        This should result in the following output:

        Minitab Express output: z distribution showing the area above 2

        The area of the z distribution that is greater than 2 is 0.0227501

        Video Walkthrough

        Select your operating system below to see a step-by-step guide for this example.

        MinitabExpress  – Proportion Greater Than a Value on a Normal Distribution

        Question: Vehicle speeds at a highway location have a normal distribution with a mean of 65 mph and a standard deviation of 5 mph. What is the probability that a randomly selected vehicle will be going more than 73 mph? 

        Let's construct a normal distribution with a mean of 65 and standard deviation of 5 to find the area greater than 73.

        To calculate a probability for values greater than a given value in Minitab Express:

        Steps
        1. On a PC: from the menu select STATISTICS > Distribution Plot
          On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
        2. Select Display Probability 
        3. For Distribution select Normal (Note: This is the default)
        4. For Mean enter 65
        5. For Standard deviation enter 5
        6. Select A specified X value
        7. Select Right tail
        8. For X value enter 73

          This should result in the following output:

          Distribution Plot - Normal, Mean=65, StDev=5; Greater Than

          On a normal distribution with a mean of 65 and standard deviation of 5, the proportion greater than 73 is 0.0547993

          In other words, 5.47993% of vehicles will be going more than 73 mph.

          Video Walkthrough

          Select your operating system below to see a step-by-step guide for this example.


          7.2.2.1 - Video Example: P(Z>0.5)

          7.2.2.1 - Video Example: P(Z>0.5)

          Question: What proportion of the z distribution is greater than z = 0.5?

          Steps
          1. On a PC: from the menu select STATISTICS > Distribution Plot
            On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
          2. Select Display Probability (Note: The default is the standard normal distribution)
          3. Select A specified X value
          4. Select Right tail
          5. For X value enter 0.5
          Video Walkthrough

          Select your operating system below to see a step-by-step guide for this example.


          7.2.3 - Proportion 'In between'

          7.2.3 - Proportion 'In between'

          MinitabExpress  – Proportion Between Two z Values

          Question: What proportion of the standard normal distribution is between a z score of 0 and a z score of 1.75?

          Recall that the standard normal distribution (i.e., distribution) has a mean of 0 and standard deviation of 1. This is the default normal distribution in Minitab Express.

          Steps
          1. On a PC: from the menu select STATISTICS > Distribution Plot
            On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
          2. Select Display Probability (Note: The default is the standard normal distribution)
          3. Select A specified X value
          4. Select Middle
          5. For X value 1 enter 0 and for X value 2 enter 1.75

            This should result in the following output:

            Standard normal distribution from Minitab Express showing that the area between 0 and 1.75 is 0.459941

            The proportion of the z distribution that is between 0 and 1.75 is 0.459941

            Video Walkthrough

            Select your operating system below to see a step-by-step guide for this example.

            MinitabExpress  – Proportion Between Values on a Normal Distirbution

            Question: Vehicle speeds at a highway location have a normal distribution with a mean of 65 mph and a standard deviation of 5 mph. What is the probability that a randomly selected vehicle will be going between 60 mph and 73 mph?

            Let's construct a normal distribution with a mean of 65 and standard deviation of 5 to find the area between 60 and 73.

            Steps
            1. On a PC: from the menu select STATISTICS > Distribution Plot
              On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
            2. Select Display Probability 
            3. For Distribution select Normal
            4. For Mean enter 65
            5. For Standard deviation enter 5
            6. Select A specified X value
            7. Select Middle
            8. For X value 1 enter 60 and for X value 2 enter 73

              This should result in the following output:

              Distribution Plot - Normal, Mean=65, StDev=5; In Between

              On a normal distribution with a mean of 65 and standard deviation of 5, the proportion between 60 and 73 is 0.786545

              In other words, 78.6545% of vehicles will be going between 60 mph and 73 mph. 

              Video Walkthrough

              Select your operating system below to see a step-by-step guide for this example.


              7.2.3.1 - Video Example: Proportion Between z -2 and +2

              7.2.3.1 - Video Example: Proportion Between z -2 and +2

              Question: What proportion of the z distribution is between -2 and 2?

              Steps
              1. On a PC: from the menu select STATISTICS > Distribution Plot
                On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
              2. Select Display Probability (Note: The default is the standard normal distribution)
              3. Select A specified X value
              4. Select Middle
              5. For X value 1 enter -2 and for X value 2 enter 2

              7.2.4 - Proportion "More Extreme Than"

              7.2.4 - Proportion "More Extreme Than"

              MinitabExpress

              Question: What proportion of the standard normal distribution is more extreme than a z value of ±2?

              Steps
              1. On a PC: from the menu select STATISTICS > Distribution Plot
                On a Mac: from the menu select Statistics > Probability Distributions > Distribution Plot
              2. Select Display Probability (Note: The default is the standard normal distribution)
              3. Select A specified X value
              4. Select Equal tails
              5. For X value enter 2

              This should result in the following output:

              Minitab Express output showing a z distribution showing the area less than -2 and greater than +2

              Video Walkthrough

              Select your operating system below to see a step-by-step guide for this example.


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