Question

In a normal distribution, what percent of the values lie: a. below the mean b. above the mean c. within one standard deviation of the mean d. within two standard deviations of the mean e. within three standard deviations of the mean

Answer 1

In a normal distribution, different percentages of values lie below, above, and within a certain number of standard deviations of the mean.

Step-by-step explanation:

The percentage of values that lie below the mean in a normal distribution is approximately 50%. This is because the distribution is symmetric, so the area under the curve to the left of the mean is the same as the area under the curve to the right of the mean.

The percentage of values that lie above the mean is also approximately 50%, for the same reason mentioned above.

Approximately 68% of the values in a normal distribution lie within one standard deviation of the mean, on both sides. This is known as the Empirical Rule or the 68-95-99.7 Rule.

Approximately 95% of the values lie within two standard deviations of the mean, on both sides.

Approximately 99.7% of the values lie within three standard deviations of the mean, on both sides.