Questions: 4 / 10 Correct Decide which of the following statements are true. There are an unlimited number of normal distributions. The y-axis is a vertical asymptote for all normal distributions. The total area under a normal distribution curve with a standard deviation of 4 is the same as the area under a normal distribution curve with a standard deviation of 12 Normal distributions are bell-shaped, but they do not have to be symmetric.

4 / 10
Correct

Decide which of the following statements are true.

There are an unlimited number of normal distributions.
The y-axis is a vertical asymptote for all normal distributions.
The total area under a normal distribution curve with a standard deviation of 4 is the same as the area under a normal distribution curve with a standard deviation of 12
Normal distributions are bell-shaped, but they do not have to be symmetric.

Transcript text: Question 5 of 10, Step 1 of 1 $4 / 10$ Correct Decide which of the following statements are true. Answer Tables Keypad Keybourd Shortcuts There are an unlimited number of normal distributions. The $y$-axis is a vertical asymptote for all normal distributions. The total area under a normal distribution curve with a standard deviation of 4 is the same as the area under a normal distribution curve with a standard deviation of 12 Normal distributions are bell-shaped, but they do not have to be symmetric. Subrnit Answer

Solution

Solution Steps

Step 1: Symmetry and Shape

Normal distributions are always symmetric and bell-shaped. The statement is false.

Step 2: Mean, Median, and Mode

For a normal distribution, the mean, median, and mode are all equal. The statement is true.

Step 3: Total Area under the Curve

The total area under a normal distribution curve is always 1. The statement is true.

Step 4: Standard Deviation and Spread

The standard deviation affects the spread of the distribution but not the total area under the curve. A positive standard deviation is expected. The statement is true.

Step 5: Inflection Points

The inflection points of a normal distribution are one standard deviation away from the mean. The statement is true.

Step 6: Asymptotes

The x-axis serves as a horizontal asymptote for normal distributions; there are no vertical asymptotes. The statement is false.