Finding Percentages in a Normal Distribution Using Z Scores and Tables

This lesson teaches how to find the percentage of a population within a certain interval using Z-scores and statistics tables. It begins with a review of the empirical rule and its limitations, then introduces Z-scores as a method to measure how far a value is from the mean. The lesson explains how to use Z-scores with statistics tables to find areas under the normal curve, converting these areas into percentages. Examples are provided to illustrate the process, including calculating the percentage of IQ scores between specific values.

What does the empirical rule state about the percentage of data within one standard deviation of the mean in a normal distribution?

• About 68%

• About 50%

• About 95%

• About 99.7%

How is a Z-score calculated?

• By adding the mean to the value

• By subtracting the mean from the value and dividing by the standard deviation

• By multiplying the value by the standard deviation

• By dividing the mean by the value

What does a Z-score of 0.9 indicate about a value?

• It is almost 1 standard deviation above the mean

• It is exactly at the mean

• It is 2 standard deviations above the mean

• It is below the mean

What is the area under the entire normal curve in a standard normal distribution?

• 3

• 2

• 1

• 0.5

How do you convert the area under the curve to a percentage?

• Subtract from 1

• Multiply by 10

• Multiply by 100

• Divide by 100

What is the Z-score for an IQ score of 80, given a mean of 100 and a standard deviation of 15?

• -0.33

• 0.33

• 1.33

• -1.33

What percentage of IQ scores fall between 80 and 105?

• 68%

• 53.75%

• 95%

• 99.7%