14.3.1. The Normal Distribution

Try these first

1. 1.

   What shape is the graph of a normal distribution?

   Hint

   Think about its symmetry and appearance.

2. 2.

   What do we call the central value around which a normal distribution is symmetrically arranged?

   Hint

   It's also known as the average.

3. 3.

   What characterizes a normal distribution?

   • A skewed distribution
   • A bell-shaped curve
   • A linear function

   Hint

   Remember, it's named after a shape associated with bells.

4. 4.

   True or False: The total area under the curve of a normal distribution is always equal to 1.

   • True
   • False

   Hint

   Think about how probabilities are defined.

5. 5.

   Given a normally distributed set with a mean of 100 and a standard deviation of 15, calculate the z-score for a value of 130.

   Hint

   Z-scores can help you understand how far away from the mean a value is.

6. 6.

   If a structural component follows a normal distribution with a mean load of 5000 N and a standard deviation of 200 N, what is the likelihood it will fail if it can only support loads of 5300 N or less?

   Hint

   Think about what it means for a value to be above the mean.