20.4. Applications of Normal Distribution

Try these first

1. 1.

   What is the empirical rule?

   Hint

   Think about how data values spread around the mean.

2. 2.

   Give an example of how normal distribution is applied in finance.

   Hint

   Consider how investors evaluate market performance.

3. 3.

   What percentage of data lies within two standard deviations from the mean according to the empirical rule?

   • 68%
   • 95%
   • 99.7%

   Hint

   Recall the three key percentages defined by the empirical rule.

4. 4.

   True or False: The normal distribution is used in quality control to determine acceptable product specifications.

   • True
   • False

   Hint

   Think about how companies maintain quality standards.

5. 5.

   A manufacturing company produces bolts with a mean diameter of 10mm and a standard deviation of 0.2mm. If the production output is normally distributed, what percentage of bolts will be within the range of 9.6mm to 10.4mm?

   Hint

   Remember to convert the measurements to Z using the mean and standard deviation.

6. 6.

   Discuss the limitations of assuming that stock returns follow a normal distribution in finance.

   Hint

   Consider real market behaviors and their characteristics.