Probability Distributions: Normal Distribution

Question 1

Normal Distribution

Answer 1

• Used to analyze data when there is an equally likely change of being above or below the mean for continuous data whose histogram fits a bell curve.
• Aka Gaussian Probability Distribution

Question 2

Normal Distribution Basic Assumptions

Answer 2

• Normal Distribution is the most widely known symmetric distribution for continuous data
• Symmetrical distribution about the mean (bell-shaped curve)
  
  • They will never be perfect unless you have an infinite data set
• Commonly used in inferential statistics
  
  • Most commonly used distribution in Six Sigma
• Family of distributions characterized by m and s
• The peak of the normal curve is an indication of the average, which is the center of process variation.
  
  • An average of a group of numbers is an indication of the central tendency
• If there is a normal curve, nothing is unduly influencing the process
• Is symmetric
  
  • Many other distributions can be symmetric under the right circumstances including Binomial and Chi Square
    
    • Do NOT assume that symmetric data is normally distributed

Question 3

When to Use Normal Distribution

Answer 3

• When data is grouped around the mean and there is an equal probability of being above or below the mean ( 50% above & 50% below the average)
• If we can transform data to behave like a normal distribution, then do it! Much easier to work with data in this shape!
  
  • Example: If we have to take the log of values, or subtract a number, or perform some other operation on the data, then do it.
• Use when the histogram fits a bell curve
• Use when the goodness-of-fit statistic is less than the selected P-value (usually 0.05)

Question 4

Normal Distribution Uses:

Answer 4

• Normal Distribution is used to test population means from sample data
• Use a histogram to determine if data are normally distributed
• Probabilistic assessments of distribution of time between independent events occurring at a constant rate
• Shape can be used to describe failure rates that are constant as a function of usage
• The standard normal or t-distribution are most likely used to compare two process means

Question 5

Normal Distribution Formula

Answer 5

• In a normal distribution, 68% of the data will occur within +/- 1 standard deviation.

Question 6

Formulas for Population mean, Variance, Standard Deviation

Answer 6

Question 7

5Ms & 1 P

Answer 7

When you have a bell shaped curve, none of the 5Ms or one P are unduly influencing the process.

Question 8

Empirical Rule

Answer 8

• 68% of our data falls within 1 std
• 95% of our data falls within 2 std
• 99.7% of our data falls within 3 std

Question 9

Normal Distribution Properties

Answer 9

• Symmetrical
• Mean, Mode, and Median are all equal