Business Statistics

1
Business Statistics

• Exercises with Normally Probabilities

2
Student Objectives

• Calculate probabilities associated with normally
  distributed random variables
• Apply normal distribution calculations to various
  decision making situations

3
First, an Announcement

• Visits this week by major firms
• Cardinal Health
• Acxiom
• Cardinal Health (Kathy White)
• Who are they?
• Why do we care?
• When/where
• Acxiom
• Who are they and what do they do?
• When/where

4
Working with Normal Distributions

• First, sketch
• Number line with
• Average (i.e., m)
• Also x value of concern
• Curve approximating histogram
• Identify areas of importance
• Then determine how many standard deviations x
  value is from m
• Now use the table
• Finally, put it all together

5
Mechanics Some Calculation Exercises

• Let x N(34,3) as with the mpg problem
• Determine
• Tail probabilities
• F(30) which is the same as P(x 30)
• P(x gt 40)
• Tail complements
• P(x gt 30)
• P(x lt 40)
• Other
• P(32 lt x lt 33)
• P(30 lt x lt 35)
• P(20 lt x lt 30)

6
Recall About the Normal Table

• The outside values are z-scores
• That is, how many standard deviations a given x
  value is from the average
• Use these values to look up probabilities
• The body of the table indicates probabilities
• Note This is not a z table!
• We can (and do) also work in reverse
• Given a probability, determine z
• Once we have z we can determine what x value
  corresponds to that probability

7
Keep In Mind

• Probability proportion of area under the normal
  curve
• What we get when we use tables is always the area
  between the mean and z standard deviations from
  the mean
• Because of symmetry
• P(x gt m) P(x lt m) 0.5000
• Tables show probabilities rounded to 4 decimal
  places
• If z lt -3.09 then probability 0.5000
• If z gt 3.09 then probability 0.5000
• Theoretically, P(x a) 0
• P(30 x 35) P(30 lt x lt 35)

8
Why Is This Important?

• Some practical applications
• Process capability analysis
• Decision analysis
• Optimization (e.g., ROP)
• Reliability studies
• Others
• Most importantly, the normal distribution is the
  basis for understanding statistical inference
• Hence, bear with this it should be apparent soon

9
Homework

• Rework (as necessary) exercises assigned from
  Chapter 5
• Work problems on Exam 3 from Spring 2000
• Review for midterm exam