Exploring the 68-95-99.7 Rule in Normal Distribution

The video tutorial explains z-scores and the normal distribution. It covers the concept of z-scores, which indicate how many standard deviations a value is from the mean. The tutorial highlights that in a normal distribution, the mean, median, and mode are equal and centered at a z-score of zero. It also discusses the symmetry of the normal distribution and how proportions of values can be calculated for different z-score ranges, such as between -1 and +1 or 1 and 2 standard deviations from the mean.

What is the central value of a z-score in a normal distribution?

• Mean

• 0

• 1

• Median

In a normal distribution, what is the z-score of a value that is one standard deviation above the mean?

• -1

• 2

• 1

• 0

What does a z-score of -2 indicate?

• Two standard deviations above the mean

• Two standard deviations below the mean

• Two units from the median

• Two units from the mode

In a normal distribution, what is the z-score of a value that is two standard deviations above the mean?

• 0

• 1

• 2

• -2

What is the proportion of values under the curve between a z-score of 0 and 1?

• 0.5000

• 0.1359

• 0.6826

• 0.3413

What percentage of values fall within a z-score of -1 to +1 in a normal distribution?

• 13.59%

• 34.13%

• 68.26%

• 50.00%

What is the proportion of values under the curve between a z-score of -1 and 0?

• 0.1359

• 0.6826

• 0.5000

• 0.3413

What is the proportion of values under the curve between a z-score of 1 and 2?

• 0.5000

• 0.3413

• 0.1359

• 0.6826

What does the symmetrical nature of the normal distribution imply about the areas under the curve?

• They are different on each side

• They are equal on both sides

• They are always zero

• They are random

What percentage of values fall between a z-score of 1 and 2 in a normal distribution?

• 50.00%

• 13.59%

• 68.26%

• 34.13%