20.2. Properties of the Normal Distribution

Try these first

1. 1.

   What shape does the graph of a normal distribution form?

   Hint

   Think about how you would draw it.

2. 2.

   True or False: The mean, median, and mode are always the same in a normal distribution.

   Hint

   Consider how data balances around the center.

3. 3.

   What characterizes the normal distribution curve?

   • Asymmetric shape
   • Symmetrical shape around the mean
   • Straight line

   Hint

   Visualize the curve when thinking about this.

4. 4.

   True or False: The total area under the normal distribution curve is equal to 2.

   • True
   • False

   Hint

   Recall the basis of probability.

5. 5.

   A company finds that the length of time its employees work each day is normally distributed with a mean of 8.5 hours and a standard deviation of 0.5 hours. What is the probability that a randomly selected employee works between 8 and 9 hours?

   Hint

   Remember to find the Z-scores first before referring to the Z-table.

6. 6.

   Explain how you would use the normal distribution to model the heights of plants in a garden, describing the steps to determine if the plant heights follow a normal distribution.

   Hint

   Consider different characteristics of the plants and how you’d measure them.