Question

Which of the following statements is true?

A. The total area under a normal distribution curve with a standard deviation of 12 is three times the area under a normal distribution.
B. The total area under a normal distribution curve with a standard deviation of 12 is six times the area under a normal distribution.
C. The total area under a normal distribution curve with a standard deviation of 12 is equal to the area under a normal distribution.
D. The total area under a normal distribution curve with a standard deviation of 12 cannot be determined from the information provided.

Answer 1

The total area under a normal distribution curve with a standard deviation of 12 is six times the area under a normal distribution.

Step-by-step explanation:

The correct statement is B. The total area under a normal distribution curve with a standard deviation of 12 is six times the area under a normal distribution.

In a normal distribution, approximately 68% of the area lies within one standard deviation of the mean, and approximately 95% of the area lies within two standard deviations of the mean.

Therefore, if the standard deviation is increased from 1 to 12, the total area under the curve will increase by a factor of approximately 6.