Question

Which of the following properties DOES NOT apply to the standard normal distribution?

1. The mean, median and mode are all equal.
2. The distribution is bi-modal.
3. The distribution is bell shaped.
4. The curve never touches the x-axis.

Answer 1

The standard normal distribution is a bell-shaped distribution with several properties. It is not bi-modal and the curve does not touch the x-axis.

Step-by-step explanation:

The standard normal distribution is a bell-shaped distribution that has several properties. Let's go through each option:

1. The mean, median, and mode are all equal: This property applies to the standard normal distribution. The mean, median, and mode are all located at the same point in a bell-shaped distribution.
2. The distribution is bi-modal: This property does NOT apply to the standard normal distribution. The standard normal distribution is unimodal, meaning it has a single peak.
3. The distribution is bell-shaped: This property applies to the standard normal distribution. The standard normal distribution has a bell-shaped curve.
4. The curve never touches the x-axis: This property applies to the standard normal distribution. The curve never touches the x-axis and extends infinitely in both directions.

Therefore, option 2 is the correct answer.