Using The Normal Distribution To Solve Business Problems

1
Using The Normal Distribution To Solve Business
Problems

• Examples Illustrated

2
The Vending Machine Example The Normal
Distribution

• Let X The amount of coffee dispensed per 7 oz.
  Cup from the vending machine.
• Assume the population mean and standard deviation
  are 5 oz. and 3/4 oz. respectively.
• Suppose also that X follows a normal distribution.

3
Whats The Chance That The Vending Machine Will
Dispense Less than 4 oz. ?

• Step 1 P(Xlt4oz.)
• Step 2 Z (4-5)/.75 -1.33
• Step 3 Draw picture of bell shaped curve.
• Step 4 Compute area under curve. Notice that the
  area between / - 1.33 of the mean is 82.30
  (rounding). Hence the area less than -1.33 is
  8.85
• Interpretation The chance of a customer going to
  the vending machine and getting less than 4 oz.
  of coffee is about 8.85.

4
Whats the Chance The Amount Of Coffee Will Be
Between 3.5 oz. and 6.5 oz. ?

• Step 1 P(3.5oz. lt X lt 6.5oz.)
• Step 2 Z1 (3.5-5)/.75 -2
• Z2 (6.5-5)/.75 2
• Step 3 Draw area under bell shaped curve.
• Step 4 Compute area under curve using normal
  table. The area / - 2 from the mean is 95.
  45.
• Interpretation The chance that a customer will
  get between 3.5 and 6.5 ounces of coffee is
  95.45.

5
Whats The Chance the Cup Will Be Over Filled?